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{"sheet":"nuRBDWS","index":0,"n_rows":24,"n_cols":7,"rows_kept":24,"cut":false,"hidden":false,"merged":[[23,4,23,5]]}
["Randomized Block Design (ANOVA: Two-Factor Without Replication)"]
[]
["SUMMARY","Count","Sum","Average","Variance"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["ANOVA"]
["Source of Variation","SS","df","MS","F","P-value","F crit"]
["Rows",null,{"$f":"COUNTA(#REF!)-2","v":-1},{"$f":"B19/C19","v":0},{"$f":"D19/D$21","v":{"$error":"#DIV/0!"}},{"$f":"_xlfn.F.DIST.RT(E19,C19,C$21)","v":{"$error":"#DIV/0!"}},{"$f":"_xlfn.F.INV.RT(G$24,C19,C$21)","v":{"$error":"#NUM!"}}]
["Columns",null,{"$f":"COUNTA(#REF!)-2","v":-1},{"$f":"B20/C20","v":0},{"$f":"D20/D$21","v":{"$error":"#DIV/0!"}},{"$f":"_xlfn.F.DIST.RT(E20,C20,C$21)","v":{"$error":"#DIV/0!"}},{"$f":"_xlfn.F.INV.RT(G$24,C20,C$21)","v":{"$error":"#NUM!"}}]
["Error",{"$f":"B23-B19-B20","v":0},{"$f":"C19*C20","v":1},{"$f":"B21/C21","v":0}]
[]
["Total",null,{"$f":"SUM(C19:C21)","v":-1}]
[null,null,null,null,"Level of significance",null,0.05]

{"sheet":"RBDWS","index":1,"n_rows":24,"n_cols":7,"rows_kept":24,"cut":false,"hidden":false,"merged":[[23,4,23,5]]}
["Randomized Block Design (ANOVA: Two-Factor Without Replication)"]
[]
["SUMMARY","Count","Sum","Average","Variance"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["ANOVA"]
["Source of Variation","SS","df","MS","F","P-value","F crit"]
["Rows",null,{"$f":"COUNTA(#REF!)-2","v":-1},{"$f":"B19/C19","v":0},{"$f":"D19/D$21","v":{"$error":"#DIV/0!"}},{"$f":"FDIST(E19,C19,C$21)","v":{"$error":"#DIV/0!"}},{"$f":"FINV(G$24,C19,C$21)","v":{"$error":"#NUM!"}}]
["Columns",null,{"$f":"COUNTA(#REF!)-2","v":-1},{"$f":"B20/C20","v":0},{"$f":"D20/D$21","v":{"$error":"#DIV/0!"}},{"$f":"FDIST(E20,C20,C$21)","v":{"$error":"#DIV/0!"}},{"$f":"FINV(G$24,C20,C$21)","v":{"$error":"#NUM!"}}]
["Error",{"$f":"B23-B19-B20","v":0},{"$f":"C19*C20","v":1},{"$f":"B21/C21","v":0}]
[]
["Total",null,{"$f":"SUM(C19:C21)","v":-1}]
[null,null,null,null,"Level of significance",null,0.05]

{"sheet":"LRWS","index":2,"n_rows":4,"n_cols":7,"rows_kept":4,"cut":false,"hidden":false,"merged":[]}
["Logistic Regression",null,null,null,null,null,"Y"]
[]
["Predictor","Coefficients","SE Coef","Z","p-Value"]
["Intercept",null,null,-1,{"$f":"2*(1-NORMSDIST(ABS(D4)))","v":0.31731050786291393}]

{"sheet":"DescSummaryWS","index":3,"n_rows":16,"n_cols":2,"rows_kept":16,"cut":false,"hidden":false,"merged":[]}
["Measures of Central Tendency, Variation, and Shape"]
[]
[null,"Variable 1"]
["Mean",{"$f":"AVERAGE(E:E)","v":{"$error":"#DIV/0!"}}]
["Median",{"$f":"MEDIAN(E:E)","v":{"$error":"#NUM!"}}]
["Mode",{"$f":"MODE(E:E)","v":{"$error":"#N/A"}}]
["Minimum",{"$f":"MIN(E:E)","v":0}]
["Maximum",{"$f":"MAX(E:E)","v":0}]
["Range",{"$f":"B8 - B7","v":0}]
["Variance",{"$f":"VAR(E:E)","v":{"$error":"#DIV/0!"}}]
["Standard Deviation",{"$f":"STDEV(E:E)","v":{"$error":"#DIV/0!"}}]
["Coeff. of Variation",{"$f":"B11/B4","v":{"$error":"#DIV/0!"}}]
["Skewness",{"$f":"SKEW(E:E)","v":{"$error":"#DIV/0!"}}]
["Kurtosis",{"$f":"KURT(E:E)","v":{"$error":"#DIV/0!"}}]
["Count",{"$f":"COUNT(E:E)","v":0}]
["Standard Error",{"$f":"B11/SQRT(B15)","v":{"$error":"#DIV/0!"}}]

{"sheet":"ATFWORWS","index":4,"n_rows":24,"n_cols":7,"rows_kept":24,"cut":false,"hidden":false,"merged":[[23,3,23,5]]}
["ANOVA: Two-Factor Without Replication"]
[]
["SUMMARY","Count","Sum","Average","Variance"]
["Rater 1",4,287,71.75,76.25]
["Rater 2",4,316,79,36.666666666666664]
["Rater 3",4,313,78.25,90.916666666666671]
["Rater 4",4,315,78.75,184.91666666666666]
["Rater 5",4,326,81.5,121]
["Rater 6",4,330,82.5,161]
[]
["Restaurant A",6,465,77.5,21.5]
["Restaurant B",6,400,66.666666666666671,23.466666666666423]
["Restaurant C",6,546,91,33.200000000000003]
["Restaurant D",6,476,79.333333333333329,23.466666666667152]
[]
[]
["ANOVA"]
["Source of Variation","SS","df","MS","F","P-value","F crit"]
["Rows",null,null,{"$f":"B19/C19","v":{"$error":"#DIV/0!"}},{"$f":"D19/D$21","v":{"$error":"#DIV/0!"}},{"$f":"FDIST(E19,C19,C$21)","v":{"$error":"#DIV/0!"}},{"$f":"FINV(G$24,C19,C$21)","v":{"$error":"#NUM!"}}]
["Columns",null,null,{"$f":"B20/C20","v":{"$error":"#DIV/0!"}},{"$f":"D20/D$21","v":{"$error":"#DIV/0!"}},{"$f":"FDIST(E20,C20,C$21)","v":{"$error":"#DIV/0!"}},{"$f":"FINV(G$24,C20,C$21)","v":{"$error":"#NUM!"}}]
["Error",{"$f":"B23-B19-B20","v":0},{"$f":"C19*C20","v":0},{"$f":"B21/C21","v":{"$error":"#DIV/0!"}}]
[]
["Total",null,{"$f":"SUM(C19:C21)","v":0}]
[null,null,null,"Level of significance",null,null,0.05]

{"sheet":"MRWS","index":5,"n_rows":19,"n_cols":12,"rows_kept":19,"cut":false,"hidden":false,"merged":[[0,10,0,13]]}
["Multiple Regression",null,null,null,null,null,null,null,null,null,"Calculations"]
[null,null,null,null,null,null,null,null,null,null,"b2, b1, b0 intercepts"]
["Regression Statistics",null,null,null,null,null,null,null,null,null,"b2, b1, b0 Standard Error"]
["Multiple R",{"$f":"SQRT(C12/C14)","v":{"$error":"#DIV/0!"}},null,null,null,null,null,null,null,null,"R Square, Standard Error"]
["R Square",{"$f":"L4","v":0},null,null,null,null,null,null,null,null,"F, Residual df"]
["Adjusted R Square",{"$f":"1-(B14/B13)*(C13/C14)","v":{"$error":"#DIV/0!"}},null,null,null,null,null,null,null,null,"Regression SS, Residual SS"]
["Standard Error",{"$f":"M4","v":0}]
["Observations",{"$f":"COUNT(#REF!)","v":0},null,null,null,null,null,null,null,null,"Confidence level",0.95]
[null,null,null,null,null,null,null,null,null,null,"t Critical Value",{"$f":"TINV(1-L8, B13)","v":{"$error":"#NUM!"}}]
["ANOVA",null,null,null,null,null,null,null,null,null,"Half Width b0",{"$f":"L$9 * C17","v":{"$error":"#NUM!"}}]
[null,"df","SS","MS","F","Significance F",null,null,null,null,"Half Width b1",{"$f":"L$9 * C18","v":{"$error":"#NUM!"}}]
["Regression",{"$f":"B14-B13","v":-1},{"$f":"L6","v":0},{"$f":"C12/B12","v":0},{"$f":"L5","v":0},{"$f":"FDIST(E12,B12,B13)","v":{"$error":"#NUM!"}},null,null,null,null,"Half Width b2",{"$f":"L$9 * C19","v":{"$error":"#NUM!"}}]
["Residual",{"$f":"M5","v":0},{"$f":"M6","v":0},{"$f":"C13/B13","v":{"$error":"#DIV/0!"}}]
["Total",{"$f":"B8-1","v":-1},{"$f":"C12+C13","v":0}]
[]
[null,"Coefficients","Standard Error","t Stat","P-value",{"$f":"\"Lower \" & TEXT(L8, \"##%\")","v":"Lower 95%"},{"$f":"\"Upper \" & TEXT(L8, \"##%\")","v":"Upper 95%"},{"$f":"F16","v":"Lower 95%"},"Upper 95%"]
["Intercept",{"$f":"N2","v":0},{"$f":"N3","v":0},{"$f":"B17/C17","v":{"$error":"#DIV/0!"}},{"$f":"TDIST(ABS(D17),B$13,2)","v":{"$error":"#DIV/0!"}},{"$f":"B17-L10","v":{"$error":"#NUM!"}},{"$f":"B17+L10","v":{"$error":"#NUM!"}},{"$error":"#NUM!"},{"$error":"#NUM!"}]
[null,{"$f":"M2","v":0},{"$f":"M3","v":0},{"$f":"B18/C18","v":{"$error":"#DIV/0!"}},{"$f":"TDIST(ABS(D18),B$13,2)","v":{"$error":"#DIV/0!"}},{"$f":"B18-L11","v":{"$error":"#NUM!"}},{"$f":"B18+L11","v":{"$error":"#NUM!"}},{"$error":"#NUM!"},{"$error":"#NUM!"}]
[null,{"$f":"L2","v":0},{"$f":"L3","v":0},{"$f":"B19/C19","v":{"$error":"#DIV/0!"}},{"$f":"TDIST(ABS(D19),B$13,2)","v":{"$error":"#DIV/0!"}},{"$f":"B19-L12","v":{"$error":"#NUM!"}},{"$f":"B19+L12","v":{"$error":"#NUM!"}},{"$error":"#NUM!"},{"$error":"#NUM!"}]

{"sheet":"SLRWS","index":6,"n_rows":18,"n_cols":12,"rows_kept":18,"cut":false,"hidden":false,"merged":[[0,10,0,12]]}
["Simple Linear Regression",null,null,null,null,null,null,null,null,null,"Calculations"]
[null,null,null,null,null,null,null,null,null,null,"b1, b0 Coefficients"]
["Regression Statistics",null,null,null,null,null,null,null,null,null,"b1, b0 Standard Error"]
["Multiple R",{"$f":"SQRT(C12/C14)","v":{"$error":"#DIV/0!"}},null,null,null,null,null,null,null,null,"R Square, Standard Error"]
["R Square",{"$f":"L4","v":0},null,null,null,null,null,null,null,null,"F, Residual df"]
["Adjusted R Square",{"$f":"1-(B14/B13)*(C13/C14)","v":{"$error":"#DIV/0!"}},null,null,null,null,null,null,null,null,"Regression SS, Residual SS"]
["Standard Error",{"$f":"M4","v":0}]
["Observations",{"$f":"COUNT(#REF!)","v":0},null,null,null,null,null,null,null,null,"Confidence level",0.95]
[null,null,null,null,null,null,null,null,null,null,"t Critical Value",{"$f":"TINV(1-L8,B13)","v":{"$error":"#NUM!"}}]
["ANOVA",null,null,null,null,null,null,null,null,null,"Half Width b0",{"$f":"L9*C17","v":{"$error":"#NUM!"}}]
[null,"df","SS","MS","F","Significance F",null,null,null,null,"Half Width b1",{"$f":"L9*C18","v":{"$error":"#NUM!"}}]
["Regression",1,{"$f":"L6","v":0},{"$f":"L6","v":0},{"$f":"L5","v":0},{"$f":"FDIST(E12,B12,B13)","v":{"$error":"#NUM!"}}]
["Residual",{"$f":"M5","v":0},{"$f":"M6","v":0},{"$f":"C13/B13","v":{"$error":"#DIV/0!"}}]
["Total",{"$f":"B12+B13","v":1},{"$f":"C12+C13","v":0}]
[]
[null,"Coefficients","Standard Error","t Stat","P-value",{"$f":"\"Lower \" & L8*100 & \"%\"","v":"Lower 95%"},{"$f":"\"Upper \" & L8*100 & \"%\"","v":"Upper 95%"},{"$f":"F16","v":"Lower 95%"},"Upper 95%"]
["Intercept",{"$f":"M2","v":0},{"$f":"M3","v":0},{"$f":"B17/C17","v":{"$error":"#DIV/0!"}},{"$f":"TDIST(ABS(D17),B13,2)","v":{"$error":"#DIV/0!"}},{"$f":"B17-L10","v":{"$error":"#NUM!"}},{"$f":"B17+L10","v":{"$error":"#NUM!"}},{"$error":"#NUM!"},{"$error":"#NUM!"}]
[null,{"$f":"L2","v":0},{"$f":"L3","v":0},{"$f":"B18/C18","v":{"$error":"#DIV/0!"}},{"$f":"TDIST(ABS(D18),B13,2)","v":{"$error":"#DIV/0!"}},{"$f":"B18-L11","v":{"$error":"#NUM!"}},{"$f":"B18+L11","v":{"$error":"#NUM!"}},{"$error":"#NUM!"},{"$error":"#NUM!"}]

{"sheet":"BESTWS","index":7,"n_rows":11,"n_cols":6,"rows_kept":11,"cut":false,"hidden":false,"merged":[[2,0,2,1]]}
["Best Subset Analysis"]
[]
["Intermediate Calculations"]
["R2T"]
["1 - R2T",{"$f":"1-B4","v":1}]
["n"]
["T",0]
["n - T",{"$f":"B6-B7","v":0}]
[]
["Model","Cp","k+1","R Square","Adj. R Square","Std. Error"]
["X1",{"$f":"((1-D11)*($B$8))/$B$5-$B$6+2*(C11)","v":0}]

{"sheet":"ATFRWS","index":8,"n_rows":31,"n_cols":7,"rows_kept":31,"cut":false,"hidden":false,"merged":[[30,3,30,5]]}
["Anova: Two-Factor With Replication"]
[]
["SUMMARY","CF1","CF2","CF3","CF4","Total"]
["RF1"]
["Count",null,{"$f":"B5","v":0},{"$f":"B5","v":0},{"$f":"B5","v":0},{"$f":"SUM(B5:E5)","v":0}]
["Sum",null,null,null,null,{"$f":"SUM(B6:E6)","v":0}]
["Average",null,null,null,null,{"$f":"AVERAGE(B7:E7)","v":{"$error":"#DIV/0!"}}]
["Variance"]
[]
["RF2"]
["Count",null,{"$f":"B11","v":0},{"$f":"B11","v":0},{"$f":"B11","v":0},{"$f":"SUM(B11:E11)","v":0}]
["Sum",null,null,null,null,{"$f":"SUM(B12:E12)","v":0}]
["Average",null,null,null,null,{"$f":"AVERAGE(B13:E13)","v":{"$error":"#DIV/0!"}}]
["Variance"]
[]
["Total"]
["Count",null,"x","x","x"]
["Sum"]
["Average"]
["Variance"]
[]
[]
["ANOVA"]
["Source of Variation","SS","df","MS","F","P-value","F crit"]
["Sample",null,1,{"$f":"B25/C25","v":0},{"$f":"D25/D$28","v":{"$error":"#DIV/0!"}},{"$f":"FDIST(E25,C25,C$28)","v":{"$error":"#DIV/0!"}},{"$f":"FINV(G$31,C25,C$28)","v":{"$error":"#NUM!"}}]
["Columns",null,{"$f":"COUNTA(3:3)-3","v":3},{"$f":"B26/C26","v":0},{"$f":"D26/D$28","v":{"$error":"#DIV/0!"}},{"$f":"FDIST(E26,C26,C$28)","v":{"$error":"#DIV/0!"}},{"$f":"FINV(G$31,C26,C$28)","v":{"$error":"#NUM!"}}]
["Interaction",{"$f":"B30-B25-B26-B28","v":0},{"$f":"C25*C26","v":3},{"$f":"B27/C27","v":0},{"$f":"D27/D$28","v":{"$error":"#DIV/0!"}},{"$f":"FDIST(E27,C27,C$28)","v":{"$error":"#DIV/0!"}},{"$error":"#NUM!"}]
["Within",null,{"$f":"(C25+1)*(C26+1)*(B5-1)","v":-8},{"$f":"B28/C28","v":0}]
[]
["Total",null,{"$f":"SUM(C25:C28)","v":-1}]
[null,null,null,"Level of significance",null,null,0.05]

{"sheet":"ASFWS","index":9,"n_rows":17,"n_cols":10,"rows_kept":17,"cut":false,"hidden":false,"merged":[[0,8,0,9],[16,3,16,5]]}
["Anova: Single Factor",null,null,null,null,null,null,null,"Calculations"]
[null,null,null,null,null,null,null,null,"c"]
["SUMMARY",null,null,null,null,null,null,null,"n",{"$f":"SUM(B5:B8)","v":0}]
["Groups","Count","Sum","Average","Variance"]
["Group 1"]
["Group 2"]
["Group 3"]
["Group 4"]
[]
[]
["ANOVA"]
["Source of Variation","SS","df","MS","F","P-value","F crit"]
["Between Groups",null,{"$f":"J2-1","v":-1},{"$f":"B13/C13","v":0},{"$f":"D13/D14","v":{"$error":"#DIV/0!"}},{"$f":"FDIST(E13,C13,C14)","v":{"$error":"#DIV/0!"}},{"$f":"FINV(G17,C13,C14)","v":{"$error":"#NUM!"}}]
["Within Groups",{"$f":"B16-B13","v":0},{"$f":"J3-J2","v":0},{"$f":"B14/C14","v":{"$error":"#DIV/0!"}}]
[]
["Total",null,{"$f":"C13+C14","v":-1}]
[null,null,null,"Level of significance",null,null,0.05]

{"sheet":"DotScaleWS","index":10,"n_rows":31,"n_cols":9,"rows_kept":31,"cut":false,"hidden":false,"merged":[[3,7,3,8],[8,7,8,8],[25,4,25,5]]}
["Data"]
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[null,{"$f":"(COUNTIF($A$2:$A$5,$A4)-1)*0.025+1-(COUNTIF($A$2:$A3,$A4)*0.025)","v":0.97499999999999998},{"$f":"AVERAGE(A:A)","v":{"$error":"#DIV/0!"}},0.7,null,null,null,{"$f":"IF(H3=INT(H3),\"Rule 1 applies\", IF(H3=CEILING(H3,0.5),\"Rule 2 applies\", \"Rule 3 applies\"))","v":"Rule 3 applies"}]
[null,{"$f":"(COUNTIF($A$2:$A$5,$A5)-1)*0.025+1-(COUNTIF($A$2:$A4,$A5)*0.025)","v":0.97499999999999998},"Median",null,null,null,{"$f":"IF(H4=\"Rule 2 applies\", \"average these ranks:\", \"use rank:\")","v":"use rank:"},{"$f":"IF(H4=\"Rule 2 applies\", FLOOR(H3,1), ROUND(H3,0))","v":0},{"$f":"IF(H4=\"Rule 2 applies\", CEILING(H3,1), \"\")","v":""}]
[null,{"$f":"(COUNTIF($A$2:$A$18,$A6)-1)*0.025+1-(COUNTIF($A$2:$A5,$A6)*0.025)","v":0.97499999999999998},{"$f":"MEDIAN(A:A)","v":{"$error":"#NUM!"}},0.95,null,null,{"$f":"IF(H4=\"Rule 2 applies\", \"average these values:\", \"value of rank:\")","v":"value of rank:"},{"$f":"SMALL(A:A,H5)","v":{"$error":"#NUM!"}},{"$f":"IF(H4=\"Rule 2 applies\", SMALL(A:A,I5), \"\")","v":""}]
[null,{"$f":"(COUNTIF($A$2:$A$18,$A7)-1)*0.025+1-(COUNTIF($A$2:$A6,$A7)*0.025)","v":0.97499999999999998},{"$f":"MEDIAN(A:A)","v":{"$error":"#NUM!"}},0.7,null,null,"first quartile:",{"$f":"IF(H4=\"Rule 2 applies\",(H6+I6)/2,H6)","v":{"$error":"#NUM!"}}]
[null,{"$f":"(COUNTIF($A$2:$A$18,$A8)-1)*0.025+1-(COUNTIF($A$2:$A7,$A8)*0.025)","v":0.97499999999999998},"1st Quartile",null,null,null,"Initial third quartile rank",{"$f":"(3*(COUNT(A:A)+1))/4","v":0.75}]
[null,{"$f":"(COUNTIF($A$2:$A$18,$A9)-1)*0.025+1-(COUNTIF($A$2:$A8,$A9)*0.025)","v":0.97499999999999998},{"$f":"H7","v":{"$error":"#NUM!"}},0.95,null,null,null,{"$f":"IF(H8=INT(H8),\"Rule 1 applies\", IF(H8=CEILING(H8,0.5),\"Rule 2 applies\", \"Rule 3 applies\"))","v":"Rule 3 applies"}]
[null,{"$f":"(COUNTIF($A$2:$A$18,$A10)-1)*0.025+1-(COUNTIF($A$2:$A9,$A10)*0.025)","v":0.97499999999999998},{"$f":"H7","v":{"$error":"#NUM!"}},0.7,null,null,{"$f":"IF(H9=\"Rule 2 applies\", \"average these ranks:\", \"use rank:\")","v":"use rank:"},{"$f":"IF(H9=\"Rule 2 applies\",FLOOR(H8,1),ROUND(H8,0))","v":1},{"$f":"IF(H9=\"Rule 2 applies\", CEILING(H8,1), \"\")","v":""}]
[null,{"$f":"(COUNTIF($A$2:$A$18,$A11)-1)*0.025+1-(COUNTIF($A$2:$A10,$A11)*0.025)","v":0.97499999999999998},"3rd Quartile",null,null,null,{"$f":"IF(H9=\"Rule 2 applies\", \"average these values:\", \"value of rank:\")","v":"value of rank:"},{"$f":"SMALL(A:A,H10)","v":{"$error":"#NUM!"}},{"$f":"IF(H9=\"Rule 2 applies\",SMALL(A:A,I10),\"\")","v":""}]
[null,{"$f":"(COUNTIF($A$2:$A$18,$A12)-1)*0.025+1-(COUNTIF($A$2:$A11,$A12)*0.025)","v":0.97499999999999998},{"$f":"H12","v":{"$error":"#NUM!"}},0.95,null,null,"third quartile:",{"$f":"IF(H9=\"Rule 2 applies\",(H11+I11)/2,H11)","v":{"$error":"#NUM!"}}]
[null,{"$f":"(COUNTIF($A$2:$A$18,$A13)-1)*0.025+1-(COUNTIF($A$2:$A12,$A13)*0.025)","v":0.97499999999999998},{"$f":"H12","v":{"$error":"#NUM!"}},0.7]
[null,{"$f":"(COUNTIF($A$2:$A$18,$A14)-1)*0.025+1-(COUNTIF($A$2:$A13,$A14)*0.025)","v":0.97499999999999998},"Std. Deviation"]
[null,{"$f":"(COUNTIF($A$2:$A$18,$A15)-1)*0.025+1-(COUNTIF($A$2:$A14,$A15)*0.025)","v":0.97499999999999998},{"$f":"STDEV(A:A)","v":{"$error":"#DIV/0!"}},{"$f":"C15*2","v":{"$error":"#DIV/0!"}},{"$f":"C15*3","v":{"$error":"#DIV/0!"}}]
[null,{"$f":"(COUNTIF($A$2:$A$18,$A16)-1)*0.025+1-(COUNTIF($A$2:$A15,$A16)*0.025)","v":0.97499999999999998},"1 Std. Dev"]
[null,{"$f":"(COUNTIF($A$2:$A$18,$A17)-1)*0.025+1-(COUNTIF($A$2:$A16,$A17)*0.025)","v":0.97499999999999998},{"$f":"$C$3-$C$15","v":{"$error":"#DIV/0!"}},0.9]
[null,{"$f":"(COUNTIF($A$2:$A$18,$A18)-1)*0.025+1-(COUNTIF($A$2:$A17,$A18)*0.025)","v":0.97499999999999998},{"$f":"$C$3+$C$15","v":{"$error":"#DIV/0!"}},0.9]
[null,null,"2 Std Dev."]
[null,null,{"$f":"$C$3-$D$15","v":{"$error":"#DIV/0!"}},0.8]
[null,null,{"$f":"$C$3+$D$15","v":{"$error":"#DIV/0!"}},0.8]
[null,null,"3 Std Dev"]
[null,null,{"$f":"$C$3-$E$15","v":{"$error":"#DIV/0!"}},0.7]
[null,null,{"$f":"$C$3+$E$15","v":{"$error":"#DIV/0!"}},0.7]
[]
[null,null,null,null,"Summary"]
[null,null,null,null,"Mean",{"$f":"C3","v":{"$error":"#DIV/0!"}}]
[null,null,null,null,"Median",{"$f":"C6","v":{"$error":"#NUM!"}}]
[null,null,null,null,"1st Quartile",{"$f":"C9","v":{"$error":"#NUM!"}}]
[null,null,null,null,"3rd Quartile",{"$f":"C12","v":{"$error":"#NUM!"}}]
[null,null,null,null,"Std. Deviation",{"$f":"C15","v":{"$error":"#DIV/0!"}}]

{"sheet":"CIPVWS","index":11,"n_rows":23,"n_cols":2,"rows_kept":23,"cut":false,"hidden":false,"merged":[[2,0,2,1],[7,0,7,1],[14,0,14,1]]}
["Confidence Interval Estimate for the Population Variance"]
[]
["Data"]
["Sample Size",2]
["Sample Standard Deviation",1]
["Confidence Level",0.95]
[]
["Intermediate Calculations"]
["Degrees of Freedom",{"$f":"B4-1","v":1}]
["Sum of Squares",{"$f":"B9*B5^2","v":1}]
["Single Tail Area",{"$f":"(1-B6)/2","v":2.5000000000000022E-2}]
["Lower Chi-Square Value",{"$f":"CHIINV(1-B11, B9)","v":9.8206911717525812E-4}]
["Upper Chi-Square Value",{"$f":"CHIINV(B11, B9)","v":5.0238861873148863}]
[]
["Results"]
["Interval Lower Limit for Variance",{"$f":"B10/B13","v":0.19904909520541297}]
["Interval Upper Limit for Variance",{"$f":"B10/B12","v":1018.2582697196677}]
[]
["Interval Lower Limit for Standard Deviation",{"$f":"SQRT(B16)","v":0.44614918492070899}]
["Interval Upper Limit for Standard Deviation",{"$f":"SQRT(B17)","v":31.910159349643926}]
[]
["Assumption:"]
["Population from which sample was drawn has an approximate normal distribution."]

{"sheet":"CSTVWS","index":12,"n_rows":28,"n_cols":2,"rows_kept":28,"cut":false,"hidden":false,"merged":[[8,0,8,1]]}
["Chi-Square Test of Hypothesis for the Variance"]
[]
["Data"]
["Null Hypothesis                        s^2=",1]
["Level of Significance",0.05]
["Sample Size",10]
["Sample Standard Deviation",2]
[]
["Intermediate Calculations"]
["Degrees of Freedom",{"$f":"B6-1","v":9}]
["Half Area",{"$f":"B5/2","v":2.5000000000000001E-2}]
["Chi-Square Statistic",{"$f":"B10*B7^2/B4","v":36}]
[]
["Two-Tail Test"]
["Lower Critical Value",{"$f":"CHIINV(1-B11,B10)","v":2.7003894999803584}]
["Upper Critical Value",{"$f":"CHIINV(B11,B10)","v":19.022767798641635}]
["p-Value",{"$f":"IF(B12<CHIINV(0.5,B10),1-CHIDIST(B12,B10),CHIDIST(B12,B10))","v":3.9646587980428506E-5}]
[{"$f":"IF(B17<$B$5/2,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Reject the null hypothesis"}]
[]
["Lower-Tail Test"]
["Lower Critical Value",{"$f":"CHIINV(1-B5,B10)","v":3.3251128430668162}]
["p-Value",{"$f":"1-CHIDIST(B12,B10)","v":0.99996035341201961}]
[{"$f":"IF(B22<$B$5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]
[]
["Upper-Tail Test"]
["Upper Critical Value",{"$f":"CHIINV(B5,B10)","v":16.918977604620451}]
["p-Value",{"$f":"CHIDIST(B12,B10)","v":3.9646587980428506E-5}]
[{"$f":"IF(B27<$B$5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Reject the null hypothesis"}]

{"sheet":"CovarianceWS","index":13,"n_rows":24,"n_cols":9,"rows_kept":24,"cut":false,"hidden":false,"merged":[[8,0,8,1],[19,0,19,1]]}
["Covariance Analysis"]
[]
["Probabilities & Outcomes:","P","X","Y"]
[]
[]
[]
["Weight Assigned to X",0.5]
[]
["Statistics"]
["E(X)",{"$f":"SUMPRODUCT(B4:B5,C4:C5)","v":0},null,null,"Calculations Area"]
["E(Y)",{"$f":"SUMPRODUCT(B4:B5,D4:D5)","v":0},null,null,"For variance and standard deviation:",null,null,null,"For covariance:"]
["Variance(X)",{"$f":"SUMPRODUCT(B4:B5,G13:G14)","v":0},null,null,"X-mu","Y-mu","(X-mu)^2","(Y-mu)^2","(X-mu)(Y-mu)"]
["Standard Deviation(X)",{"$f":"SQRT(B12)","v":0},null,null,{"$f":"C4-$B$10","v":0},{"$f":"D4-$B$11","v":0},{"$f":"E13^2","v":0},{"$f":"F13^2","v":0},{"$f":"E13*F13","v":0}]
["Variance(Y)",{"$f":"SUMPRODUCT(B4:B5,H13:H14)","v":0},null,null,{"$f":"C5-$B$10","v":0},{"$f":"D5-$B$11","v":0},{"$f":"E14^2","v":0},{"$f":"F14^2","v":0},{"$f":"E14*F14","v":0}]
["Standard Deviation(Y)",{"$f":"SQRT(B14)","v":0}]
["Covariance(XY)",{"$f":"SUMPRODUCT(B4:B5,I13:I14)","v":0}]
["Variance(X+Y)",{"$f":"B12+B14+2*B16","v":0}]
["Standard Deviation(X+Y)",{"$f":"SQRT(B17)","v":0}]
[]
["Portfolio Management"]
["Weight Assigned to X",{"$f":"B7","v":0.5}]
["Weight Assigned  to Y",{"$f":"1-B21","v":0.5}]
["Portfolio Expected Return",{"$f":"B21*B10+B22*B11","v":0}]
["Portfolio Risk",{"$f":"SQRT(B21^2*B12+B22^2*B14+2*B21*B22*B16)","v":0}]

{"sheet":"TSPTWS","index":14,"n_rows":29,"n_cols":5,"rows_kept":29,"cut":false,"hidden":false,"merged":[[14,3,14,4],[23,0,23,1],[25,0,25,1],[28,0,28,1],[2,0,2,1],[6,0,6,1],[14,0,14,1],[18,0,18,1],[20,0,20,1]]}
["Paired t Test"]
[]
["Data"]
["Hypothesized Mean Difference",0]
["Level of significance",0.05]
[]
["Intermediate Calculations"]
["Sample Size",2]
["DBar",1]
["Degrees of Freedom",{"$f":"B8-1","v":1}]
["SD",1]
["Standard Error",{"$f":"B11/SQRT(B8)","v":0.70710678118654746}]
["t Test Statistic",{"$f":"(B9-B4)/B12","v":1.4142135623730951}]
[]
["Two-Tail Test",null,null,"TDIST Calculations"]
["Lower Critical Value",{"$f":"-TINV(B5,B10)","v":-12.706204736174707},null,"TDIST",{"$f":"TDIST(ABS(B13),B10,1)","v":0.19591327601530362}]
["Upper Critical Value",{"$f":"TINV(B5,B10)","v":12.706204736174707},null,"1-TDIST",{"$f":"1-E16","v":0.80408672398469638}]
["p-Value",{"$f":"TDIST(ABS(B13),B10,2)","v":0.39182655203060723}]
[{"$f":"IF(B18 < B5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]
[]
["Lower-Tail Test"]
["Lower Critical Value",{"$f":"-TINV(2*B5,B10)","v":-6.3137515146750438}]
["p-Value",{"$f":"IF(B13<0,E16,E17)","v":0.80408672398469638}]
[{"$f":"IF(B23 < B5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]
[]
["Upper-Tail Test"]
["Upper Critical Value",{"$f":"TINV(2*B5,B10)","v":6.3137515146750438}]
["p-Value",{"$f":"IF(B13<0,E17,E16)","v":0.19591327601530362}]
[{"$f":"IF(B28 < B5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]

{"sheet":"TSTTSVWS","index":15,"n_rows":38,"n_cols":5,"rows_kept":38,"cut":false,"hidden":false,"merged":[[2,0,2,1],[14,0,14,1],[14,3,14,4]]}
["Separate-Variances t Test for the Difference Between Two Means"]
["(assumes unequal population variances)"]
["Data"]
["Hypothesized Difference",0]
["Level of Significance",0.05]
["Population 1 Sample"]
["Sample Size",10]
["Sample Mean",50.3]
["Sample Standard Deviation",18.726400000000002]
["Population 2 Sample"]
["Sample Size",10]
["Sample Mean",72]
["Sample Standard Deviation",12.5433]
[]
["Intermediate Calculations",null,null,"Calculations Area"]
["Numerator of Degrees of Freedom",{"$f":"(E18+E19)^2","v":2580.7663091415102},null,"Pop. 1 Sample Variance",{"$f":"B9^2","v":350.67805696000005}]
["Denominator of Degrees of Freedom",{"$f":"(E18^2)/(B7-1)+(E19^2)/(B11-1)","v":164.14356128363124},null,"Pop. 2 Sample Variance",{"$f":"B13^2","v":157.33437489000002}]
["Total Degrees of Freedom",{"$f":"B16/B17","v":15.722616768878828},null,"Pop. 1 Sample Var./Sample Size",{"$f":"E16/B7","v":35.067805696000008}]
["Degrees of Freedom",{"$f":"INT(B18)","v":15},null,"Pop. 2 Sample Var./Sample Size",{"$f":"E17/B11","v":15.733437489000002}]
["Standard Error",{"$f":"SQRT(E18+E19)","v":7.1274990834794227},null,"For one-tailed tests:"]
["Difference in Sample Means",{"$f":"B8-B12","v":-21.700000000000003},null,"TDIST value",{"$f":"TDIST(ABS(B22),B19,1)","v":4.0970529046962323E-3}]
["Separate-Variance t Test Statistic",{"$f":"(B21-B4)/B20","v":-3.0445461649090442},null,"1-TDIST value",{"$f":"1-E21","v":0.9959029470953038}]
[]
["Two-Tail Test"]
["Lower Critical Value",{"$f":"-(TINV(B5,B19))","v":-2.1314495455597742}]
["Upper Critical Value",{"$f":"TINV(B5,B19)","v":2.1314495455597742}]
["p-Value",{"$f":"TDIST(ABS(B22),B19,2)","v":8.1941058093924646E-3}]
[{"$f":"IF(B27<B5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Reject the null hypothesis"}]
[]
["Lower-Tail Test "]
["Lower Critical Value",{"$f":"-(TINV(2*B5,B19))","v":-1.7530503556925723}]
["p-Value",{"$f":"IF(B22<0,E21,E22)","v":4.0970529046962323E-3}]
[{"$f":"IF(B32<B5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Reject the null hypothesis"}]
[]
["Upper-Tail Test"]
["Upper Critical Value",{"$f":"(TINV(2*B5,B19))","v":1.7530503556925723}]
["p-Value",{"$f":"IF(B22<0,E22,E21)","v":0.9959029470953038}]
[{"$f":"IF(B37<B5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]

{"sheet":"TSTTWS","index":16,"n_rows":38,"n_cols":5,"rows_kept":38,"cut":false,"hidden":false,"merged":[[14,0,14,1],[2,0,2,1],[2,3,2,4],[3,3,3,4],[5,3,5,4],[8,3,8,4],[13,3,13,4]]}
["Pooled-Variance t Test for the Difference Between Two Means"]
["(assumes equal population variances)"]
["Data",null,null,"Confidence Interval Estimate "]
["Hypothesized Difference",0,null,"for the Difference Between Two Means"]
["Level of Significance",0.05]
["Population 1 Sample",null,null,"Data"]
["Sample Size",10,null,"Confidence Level",0.95]
["Sample Mean",1]
["Sample Standard Deviation",1,null,"Intermediate Calculations"]
["Population 2 Sample",null,null,"Degrees of Freedom",{"$f":"B16+B17","v":18}]
["Sample Size",10,null,"t Value",{"$f":"TINV(1-E7,E10)","v":2.1009220402410378}]
["Sample Mean",2,null,"Interval Half Width",{"$f":"(E11*SQRT(B19*(1/B7+1/B11)))","v":1.4855762213987147}]
["Sample Standard Deviation",2]
[null,null,null,"Confidence Interval"]
["Intermediate Calculations",null,null,"Interval Lower Limit",{"$f":"B21-E12","v":-2.4855762213987145}]
["Population 1 Sample Degrees of Freedom",{"$f":"B7-1","v":9},null,"Interval Upper Limit",{"$f":"B21+E12","v":0.4855762213987147}]
["Population 2 Sample Degrees of Freedom",{"$f":"B11-1","v":9}]
["Total Degrees of Freedom",{"$f":"B16+B17","v":18}]
["Pooled Variance",{"$f":"((B16*B9^2)+(B17*B13^2))/B18","v":2.5}]
["Standard Error",{"$f":"SQRT(B19*(1/B7+1/B11))","v":0.70710678118654757}]
["Difference in Sample Means",{"$f":"B8-B12","v":-1}]
["t Test Statistic",{"$f":"(B21-B4)/B20","v":-1.4142135623730949}]
[]
["Two-Tail Test"]
["Lower Critical Value",{"$f":"-(TINV(B5,B18))","v":-2.1009220402410378}]
["Upper Critical Value",{"$f":"TINV(B5,B18)","v":2.1009220402410378}]
["p-Value",{"$f":"TDIST(ABS(B22),B18,2)","v":0.1743634883988705}]
[{"$f":"IF(B27<$B$5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]
[]
["Lower-Tail Test ",null,null,"Calculations Area"]
["Lower Critical Value",{"$f":"-(TINV(2*B5,B18))","v":-1.7340636066175394},null,"For one-tailed tests:"]
["p-Value",{"$f":"IF(B22<0,E32,E33)","v":8.7181744199435252E-2},null,"TDIST value",{"$f":"TDIST(ABS(B22),B18,1)","v":8.7181744199435252E-2}]
[{"$f":"IF(B32<$B$5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"},null,null,"1-TDIST value",{"$f":"1-E32","v":0.91281825580056475}]
[]
["Upper-Tail Test"]
["Upper Critical Value",{"$f":"(TINV(2*B5,B18))","v":1.7340636066175394}]
["p-Value",{"$f":"IF(B22<0,E33,E32)","v":0.91281825580056475}]
[{"$f":"IF(B37<$B$5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]

{"sheet":"TSZTWS","index":17,"n_rows":34,"n_cols":2,"rows_kept":34,"cut":false,"hidden":false,"merged":[[25,0,25,1],[28,0,28,1],[30,0,30,1],[33,0,33,1],[2,0,2,1],[5,0,5,1],[9,0,9,1],[14,0,14,1],[19,0,19,1],[23,0,23,1]]}
["Z Test for Differences in Two Means"]
[]
["Data"]
["Hypothesized Difference",0]
["Level of Significance",0.05]
["Population 1 Sample"]
["Sample Size",25]
["Sample Mean",5]
["Population Standard Deviation",3]
["Population 2 Sample"]
["Sample Size",45]
["Sample Mean",8]
["Population Standard Deviation",4]
[]
["Intermediate Calculations"]
["Difference in Sample Means",{"$f":"B8-B12","v":-3}]
["Standard Error of the Difference in Means",{"$f":"SQRT(((B9 ^ 2) / B7) + (B13 ^ 2) / B11)","v":0.84590516936330129}]
["Z-Test Statistic",{"$f":"(B16-B4)/B17","v":-3.546496828075953}]
[]
["Two-Tail Test"]
["Lower Critical Value",{"$f":"NORMSINV(B5/2)","v":-1.9599639845400538}]
["Upper Critical Value",{"$f":"NORMSINV(1-(B5/2))","v":1.9599639845400536}]
["p-Value",{"$f":"2*(1-NORMSDIST(ABS(B18)))","v":3.9038944200298076E-4}]
[{"$f":"IF(B23<$B$5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Reject the null hypothesis"}]
[]
["Lower-Tail Test"]
["Lower Critical Value",{"$f":"NORMSINV(B5)","v":-1.6448536269514726}]
["p-Value",{"$f":"NORMSDIST(B18)","v":1.9519472100144403E-4}]
[{"$f":"IF(B28 < $B$5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Reject the null hypothesis"}]
[]
["Upper-Tail Test"]
["Upper Critical Value",{"$f":"NORMSINV(1-B5)","v":1.6448536269514715}]
["p-Value",{"$f":"1-NORMSDIST(B18)","v":0.99980480527899851}]
[{"$f":"IF(B33<$B$5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]

{"sheet":"TSZTPWS","index":18,"n_rows":34,"n_cols":5,"rows_kept":34,"cut":false,"hidden":false,"merged":[[13,3,13,4],[2,0,2,1],[2,3,2,4],[3,3,3,4],[5,3,5,4],[8,3,8,4],[12,0,12,1]]}
["Z Test for Differences in Two Proportions"]
[]
["Data",null,null,"Confidence Interval Estimate "]
["Hypothesized Difference",0,null,"of the Difference Between Two Proportions"]
["Level of Significance",0.05]
["Group 1",null,null,"Data"]
["Number of Items of Interest",1,null,"Confidence Level",0.95]
["Sample Size",10]
["Group 2",null,null,"Intermediate Calculations"]
["Number of Items of Interest",2,null,"Z Value",{"$f":"NORMSINV((1-E7)/2)","v":-1.9599639845400536}]
["Sample Size",20,null,"Std. Error of the Diff. between two Proportions",{"$f":"SQRT((B14*(1-B14)/B8)+(B15*(1-B15)/B11))","v":0.11618950038622251}]
[null,null,null,"Interval Half Width",{"$f":"ABS(E10*E11)","v":0.22772723613869877}]
["Intermediate Calculations"]
["Group 1 Proportion",{"$f":"B7/B8","v":0.1},null,"Confidence Interval"]
["Group 2 Proportion",{"$f":"B10/B11","v":0.1},null,"Interval Lower Limit",{"$f":"B16-E12","v":-0.22772723613869877}]
["Difference in Two Proportions",{"$f":"B14-B15","v":0},null,"Interval Upper Limit",{"$f":"B16+E12","v":0.22772723613869877}]
["Average Proportion",{"$f":"(B7+B10)/(B8+B11)","v":0.1}]
["Z Test Statistic",{"$f":"(B16-B4)/SQRT(B17*(1-B17)*(1/B8+1/B11))","v":0}]
[]
["Two-Tail Test"]
["Lower Critical Value",{"$f":"NORMSINV(B5/2)","v":-1.9599639845400538}]
["Upper Critical Value",{"$f":"NORMSINV(1-B5/2)","v":1.9599639845400536}]
["p-Value",{"$f":"2*(1-NORMSDIST(ABS(B18)))","v":1}]
[{"$f":"IF(B23<$B$5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]
[]
["Lower-Tail Test"]
["Lower Critical Value",{"$f":"NORMSINV(B5)","v":-1.6448536269514726}]
["p-Value",{"$f":"NORMSDIST(B18)","v":0.5}]
[{"$f":"IF(B28<$B$5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]
[]
["Upper-Tail Test"]
["Upper Critical Value",{"$f":"NORMSINV(1-B5)","v":1.6448536269514715}]
["p-Value",{"$f":"1-NORMSDIST(B18)","v":0.5}]
[{"$f":"IF(B33<$B$5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]

{"sheet":"TSFTWS","index":19,"n_rows":28,"n_cols":5,"rows_kept":28,"cut":false,"hidden":false,"merged":[[2,0,2,1],[11,0,11,1]]}
["F Test for Differences in Two Variances"]
[]
["Data"]
["Level of Significance",0.05]
["Larger-Variance Sample"]
["Sample Size",10]
["Sample Variance",1]
["Smaller-Variance Sample"]
["Sample Size",10]
["Sample Variance",1]
[]
["Intermediate Calculations"]
["F Test Statistic",{"$f":"B7/B10","v":1}]
["Population 1 Sample Degrees of Freedom",{"$f":"B6-1","v":9}]
["Population 2 Sample Degrees of Freedom",{"$f":"B9-1","v":9}]
[null,null,null,"Calculations Area"]
["Two-Tail Test",null,null,"FDIST value",{"$f":"FDIST(B13,B14,B15)","v":0.49999999999999989}]
["Upper Critical Value",{"$f":"FINV(B4/2,B14,B15)","v":4.0259941582829777}]
["p-Value",{"$f":"2*E17","v":0.99999999999999978}]
[{"$f":"IF(B19<B4,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]
[]
["Upper-Tail Test"]
["Upper Critical Value",{"$f":"FINV(B4,B14,B15)","v":3.17889310445827}]
["p-Value",{"$f":"E17","v":0.49999999999999989}]
[{"$f":"IF(B24<B4,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]
[]
[{"$f":"IF(B7<B10,\"Error: Review your entries for cells B6:B7 and B9:B10.\",\"\")","v":""}]
[{"$f":"IF(B7<B10,\"You entered the largest standard deviation as part of the Smaller-Variance Sample.\",\"\")","v":""}]

{"sheet":"WilcoxonWS","index":20,"n_rows":34,"n_cols":2,"rows_kept":34,"cut":false,"hidden":false,"merged":[[12,0,12,1]]}
["Wilcoxon Rank Sum Test for Differences in Two Medians"]
[]
["Data"]
["Level of Significance",0.05]
[]
["Population 1 Sample"]
["Sample Size",1]
["Sum of Ranks",1]
["Population 2 Sample"]
["Sample Size",1]
["Sum of Ranks",1]
[]
["Intermediate Calculations"]
["Total Sample Size n",{"$f":"B7+B10","v":2}]
["T1 Test Statistic",{"$f":"IF(B7<=B10,B8,B11)","v":1}]
["T1 Mean",{"$f":"IF(B7<=B10,B7*(B14+1)/2,B10*(B14+1)/2)","v":1.5}]
["Standard Error of T1",{"$f":"SQRT(B7*B10*(B14+1)/12)","v":0.5}]
["Z Test Statistic",{"$f":"(B15-B16)/B17","v":-1}]
[]
["Two-Tail Test"]
["Lower Critical Value",{"$f":"NORMSINV(B4/2)","v":-1.9599639845400538}]
["Upper Critical Value",{"$f":"NORMSINV(1-B4/2)","v":1.9599639845400536}]
["p-Value",{"$f":"2*(1-NORMSDIST(ABS(B18)))","v":0.31731050786291393}]
[{"$f":"IF(B23<$B$4,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]
[]
["Lower-Tail Test"]
["Lower Critical Value",{"$f":"NORMSINV(B4)","v":-1.6448536269514726}]
["p-Value",{"$f":"NORMSDIST(B18)","v":0.15865525393145699}]
[{"$f":"IF(B28<$B$4,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]
[]
["Upper-Tail Test"]
["Upper Critical Value",{"$f":"NORMSINV(1-B4)","v":1.6448536269514715}]
["p-Value",{"$f":"1-NORMSDIST(B18)","v":0.84134474606854304}]
[{"$f":"IF(B33<$B$4,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]

{"sheet":"ZTPWS","index":21,"n_rows":28,"n_cols":2,"rows_kept":28,"cut":false,"hidden":false,"merged":[[2,0,2,1],[8,0,8,1]]}
["Z Test of Hypothesis for the Proportion"]
[]
["Data"]
["Null Hypothesis            p =",0.1]
["Level of Significance",0.05]
["Number of Items of Interest",11]
["Sample Size",200]
[]
["Intermediate Calculations"]
["Sample Proportion",{"$f":"B6/B7","v":5.5E-2}]
["Standard Error",{"$f":"SQRT(B4*(1-B4)/B7)","v":2.1213203435596427E-2}]
["Z Test Statistic",{"$f":"(B10-B4)/B11","v":-2.1213203435596428}]
[]
["Two-Tail Test"]
["Lower Critical Value",{"$f":"NORMSINV(B5/2)","v":-1.9599639845400538}]
["Upper Critical Value",{"$f":"NORMSINV(1-B5/2)","v":1.9599639845400536}]
["p-Value",{"$f":"2*(1-NORMSDIST(ABS(B12)))","v":3.3894853524689239E-2}]
[{"$f":"IF(B17<$B$5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Reject the null hypothesis"}]
[]
["Lower-Tail Test"]
["Lower Critical Value",{"$f":"NORMSINV(B5)","v":-1.6448536269514726}]
["p-Value",{"$f":"NORMSDIST(B12)","v":1.6947426762344623E-2}]
[{"$f":"IF(B22<$B$5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Reject the null hypothesis"}]
[]
["Upper-Tail Test"]
["Upper Critical Value",{"$f":"NORMSINV(1-B5)","v":1.6448536269514715}]
["p-Value",{"$f":"1-NORMSDIST(B12)","v":0.98305257323765538}]
[{"$f":"IF(B27<$B$5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]

{"sheet":"TTMeanWS","index":22,"n_rows":29,"n_cols":5,"rows_kept":29,"cut":false,"hidden":false,"merged":[[2,0,2,1],[9,0,9,1]]}
["t Test for the Hypothesis of the Mean"]
[]
["Data"]
["Null Hypothesis                m=",120]
["Level of Significance",0.05]
["Sample Size",2]
["Sample Mean",1]
["Sample Standard Deviation",1]
[]
["Intermediate Calculations"]
["Standard Error of the Mean",{"$f":"B8/SQRT(B6)","v":0.70710678118654746}]
["Degrees of Freedom",{"$f":"B6-1","v":1}]
["t Test Statistic",{"$f":"(B7-B4)/B11","v":-168.29141392239833}]
[]
["Two-Tail Test"]
["Lower Critical Value",{"$f":"-(TINV(B5,B12))","v":-12.706204736174707}]
["Upper Critical Value",{"$f":"TINV(B5,B12)","v":12.706204736174707}]
["p-Value",{"$f":"TDIST(ABS(B13),B12,2)","v":3.7827971436405097E-3}]
[{"$f":"IF(B18<$B$5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Reject the null hypothesis"}]
[null,null,null,"Calculations Area"]
["Lower-Tail Test",null,null,"For one-tailed tests:"]
["Lower Critical Value",{"$f":"-(TINV(2*B5,B12))","v":-6.3137515146750438},null,"TDIST value",{"$f":"TDIST(ABS(B13),B12,1)","v":1.8913985718202549E-3}]
["p-Value",{"$f":"IF(B13<0,E22,E23)","v":1.8913985718202549E-3},null,"1-TDIST value",{"$f":"1-E22","v":0.9981086014281797}]
[{"$f":"IF(B23<$B$5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Reject the null hypothesis"}]
[]
["Upper-Tail Test"]
["Upper Critical Value",{"$f":"(TINV(2*B5,B12))","v":6.3137515146750438}]
["p-Value",{"$f":"IF(B13<0,E23,E22)","v":0.9981086014281797}]
[{"$f":"IF(B28<$B$5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]

{"sheet":"ZTMeanWS","index":23,"n_rows":28,"n_cols":2,"rows_kept":28,"cut":false,"hidden":false,"merged":[[2,0,2,1],[9,0,9,1]]}
["Z Test of the Hypothesis for the Mean"]
[]
["Data"]
["Null Hypothesis                       m=",1]
["Level of Significance",0.05]
["Population Standard Deviation",2]
["Sample Size",10]
["Sample Mean",1]
[]
["Intermediate Calculations"]
["Standard Error of the Mean",{"$f":"B6/SQRT(B7)","v":0.63245553203367588}]
["Z Test Statistic",{"$f":"(B8-B4)/B11","v":0}]
[]
["Two-Tail Test"]
["Lower Critical Value",{"$f":"NORMSINV(B5/2)","v":-1.9599639845400538}]
["Upper Critical Value",{"$f":"NORMSINV(1-B5/2)","v":1.9599639845400536}]
["p-Value",{"$f":"2*(1-NORMSDIST(ABS(B12)))","v":1}]
[{"$f":"IF(B17<$B$5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]
[]
["Lower-Tail Test"]
["Lower Critical Value",{"$f":"NORMSINV(B5)","v":-1.6448536269514726}]
["p-Value",{"$f":"NORMSDIST(B12)","v":0.5}]
[{"$f":"IF(B22<$B$5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]
[]
["Upper-Tail Test"]
["Upper Critical Value",{"$f":"NORMSINV(1-B5)","v":1.6448536269514715}]
["p-Value",{"$f":"1-NORMSDIST(B12)","v":0.5}]
[{"$f":"IF(B27<$B$5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]

{"sheet":"CITDWS","index":24,"n_rows":21,"n_cols":5,"rows_kept":21,"cut":false,"hidden":false,"merged":[[2,0,2,1],[7,0,7,1],[18,0,18,1]]}
["Confidence Interval Estimate for the Total Difference"]
[]
["Data"]
["Population Size",5000]
["Sample Size",100]
["Confidence Level",0.95]
[]
["Intermediate Calculations"]
["Sum of Differences","=SUM(Data!A:A)",null,"Calculations Area"]
["Average Difference in Sample",{"$f":"B9/B5","v":{"$error":"#VALUE!"}},null,"For standard deviation of differences:"]
["Total Difference",{"$f":"B4*B10","v":{"$error":"#VALUE!"}},null,"Number of Differences Not = 0","=COUNT(Data!A:A)"]
["Standard Deviation of Differences",{"$f":"SQRT(E16)","v":{"$error":"#VALUE!"}},null,"Number of Differences = 0",{"$f":"B5-E11","v":{"$error":"#VALUE!"}}]
["FPC Factor",{"$f":"SQRT((B4-B5)/(B4-1))","v":0.99004850346225037},null,"SS for Differences Not = 0","=SUM(Data!B:B)"]
["Standard Error of the Total Diff.",{"$f":"(B4*B12*B13)/SQRT(B5)","v":{"$error":"#VALUE!"}},null,"SS for Differences = 0",{"$f":"E12*(-B10)^2","v":{"$error":"#VALUE!"}}]
["Degrees of Freedom",{"$f":"B5-1","v":99},null,"Sum of Squares",{"$f":"E13+E14","v":{"$error":"#VALUE!"}}]
["t Value",{"$f":"TINV(1-B6,B15)","v":1.9842169515864165},null,"Variance of Differences",{"$f":"E15/B15","v":{"$error":"#VALUE!"}}]
["Interval Half Width",{"$f":"B16*B14","v":{"$error":"#VALUE!"}}]
[]
["Confidence Interval"]
["Interval Lower Limit",{"$f":"B11-B17","v":{"$error":"#VALUE!"}}]
["Interval Upper Limit",{"$f":"B11+B17","v":{"$error":"#VALUE!"}}]

{"sheet":"CIPTWS","index":25,"n_rows":20,"n_cols":2,"rows_kept":20,"cut":false,"hidden":false,"merged":[[9,0,9,1],[17,0,17,1]]}
["Confidence Interval Estimate for the Population Total"]
[]
["Data"]
["Population Size",5000]
["Sample Mean",100]
["Sample Size",100]
["Sample Standard Deviation",20]
["Confidence Level",0.95]
[]
["Intermediate Calculations"]
["Population Total",{"$f":"B4*B5","v":500000}]
["FPC Factor",{"$f":"SQRT((B4-B6)/(B4-1))","v":0.99004850346225037}]
["Standard Error of the Total",{"$f":"(B4*B7*B12)/SQRT(B6)","v":9900.485034622503}]
["Degrees of Freedom",{"$f":"B6-1","v":99}]
["t Value",{"$f":"TINV(1-B8,B14)","v":1.9842169515864165}]
["Interval Half Width",{"$f":"B15*B13","v":19644.7102346256}]
[]
["Confidence Interval"]
["Interval Lower Limit",{"$f":"B11-B16","v":480355.28976537439}]
["Interval Upper Limit",{"$f":"B11+B16","v":519644.71023462561}]

{"sheet":"SSPWS","index":26,"n_rows":19,"n_cols":2,"rows_kept":19,"cut":false,"hidden":false,"merged":[[7,0,7,1],[11,0,11,1]]}
["Sample Size for Estimating the Proportion"]
[]
["Data"]
["Estimate of True Proportion",0.15]
["Sampling Error",7.0000000000000007E-2]
["Confidence Level",0.95]
[]
["Intermediate Calculations"]
["Z Value",{"$f":"NORMSINV((1-B6)/2)","v":-1.9599639845400536}]
["Calculated Sample Size ",{"$f":"(B9^2*B4*(1-B4))/B5^2","v":99.956326456836862}]
[]
["Result"]
["Sample Size Needed",{"$f":"ROUNDUP(B10,0)","v":100}]
[]
[]
["Finite Populations"]
["Population Size",5000]
["Calculated Sample Size",{"$f":"(B10*B17)/(B10+B17-1)","v":98.016456758215185}]
["Sample Size Needed",{"$f":"ROUNDUP(B18,0)","v":99}]

{"sheet":"SSMWS","index":27,"n_rows":19,"n_cols":2,"rows_kept":19,"cut":false,"hidden":false,"merged":[[7,0,7,1],[11,0,11,1]]}
["Sample Size for Estimating the Mean"]
[]
["Data"]
["Population Standard Deviation",25]
["Sampling Error",5]
["Confidence Level",0.95]
[]
["Intemediate Calculations"]
["Z Value",{"$f":"NORMSINV((1-B6)/2)","v":-1.9599639845400536}]
["Calculated Sample Size ",{"$f":"((B9*B4)/B5)^2","v":96.036470517353109}]
[]
["Result"]
["Sample Size Needed",{"$f":"ROUNDUP(B10,0)","v":97}]
[]
[]
["Finite Populations"]
["Population Size",5000]
["Sample Size with FPC",{"$f":"(B10*B17)/(B10+B17-1)","v":94.245125695441288}]
["Sample Size Needed",{"$f":"ROUNDUP(B18,0)","v":95}]

{"sheet":"CIPWS","index":28,"n_rows":24,"n_cols":2,"rows_kept":24,"cut":false,"hidden":false,"merged":[[7,0,7,1],[13,0,13,1]]}
["Confidence Interval Estimation for the Proportion"]
[]
["Data"]
["Sample Size",100]
["Number of Successes",10]
["Confidence Level",0.95]
[]
["Intermediate Calculations"]
["Sample Proportion",{"$f":"B5/B4","v":0.1}]
["Z Value",{"$f":"NORMSINV((1-B6)/2)","v":-1.9599639845400536}]
["Standard Error of the Proportion",{"$f":"SQRT(B9*(1-B9)/B4)","v":3.0000000000000002E-2}]
["Interval Half Width",{"$f":"ABS(B10*B11)","v":5.8798919536201616E-2}]
[]
["Confidence Interval"]
["Interval Lower Limit",{"$f":"B9-B12","v":4.120108046379839E-2}]
["Interval Upper Limit",{"$f":"B9+B12","v":0.15879891953620162}]
[]
[]
["Finite Populations"]
["Population Size",5000]
["FPC Factor",{"$f":"SQRT((B20-B4)/(B20-1))","v":0.99004850346225037}]
["Interval Half Width",{"$f":"B12*B21","v":5.821378229201369E-2}]
["Interval Lower Limit",{"$f":"B9-B22","v":4.1786217707986316E-2}]
["Interval Upper Limit",{"$f":"B9+B22","v":0.15821378229201369}]

{"sheet":"CIMSUWS","index":29,"n_rows":25,"n_cols":2,"rows_kept":25,"cut":false,"hidden":false,"merged":[[8,0,8,1],[14,0,14,1]]}
["Confidence Interval Estimate for the Mean"]
[]
["Data"]
["Sample Standard Deviation",20]
["Sample Mean",10]
["Sample Size",100]
["Confidence Level",0.95]
[]
["Intermediate Calculations"]
["Standard Error of the Mean",{"$f":"B4/SQRT(B6)","v":2}]
["Degrees of Freedom",{"$f":"B6-1","v":99}]
["t Value",{"$f":"TINV(1-B7,B11)","v":1.9842169515864165}]
["Interval Half Width",{"$f":"B12*B10","v":3.9684339031728331}]
[]
["Confidence Interval"]
["Interval Lower Limit",{"$f":"B5-B13","v":6.0315660968271665}]
["Interval Upper Limit",{"$f":"B5+B13","v":13.968433903172834}]
[]
[]
["Finite Populations"]
["Population Size",5000]
["FPC Factor",{"$f":"SQRT((B21-B6)/(B21-1))","v":0.99004850346225037}]
["Interval Half Width",{"$f":"B13*B22","v":3.9289420469251204}]
["Interval Lower Limit",{"$f":"B5-B23","v":6.0710579530748792}]
["Interval Upper Limit",{"$f":"B5+B23","v":13.928942046925121}]

{"sheet":"CIMSKWS","index":30,"n_rows":24,"n_cols":2,"rows_kept":24,"cut":false,"hidden":false,"merged":[[8,0,8,1],[13,0,13,1]]}
["Confidence Interval Estimate for the Mean"]
[]
["Data"]
["Population Standard Deviation",0.02]
["Sample Mean",10]
["Sample Size",100]
["Confidence Level",0.95]
[]
["Intermediate Calculations"]
["Standard Error of the Mean",{"$f":"B4/SQRT(B6)","v":2E-3}]
["Z Value",{"$f":"NORMSINV((1-B7)/2)","v":-1.9599639845400536}]
["Interval Half Width",{"$f":"CONFIDENCE(1-B7,B4,B6)","v":3.9199279690801071E-3}]
[]
["Confidence Interval"]
["Interval Lower Limit",{"$f":"B5-B12","v":9.9960800720309191}]
["Interval Upper Limit",{"$f":"B5+B12","v":10.003919927969081}]
[]
[]
["Finite Populations"]
["Population Size",10000]
["FPC Factor",{"$f":"SQRT((B20-B6)/(B20-1))","v":0.99503719020998915}]
["Interval Half Width",{"$f":"B12*B21","v":3.9004741121790188E-3}]
["Interval Lower Limit",{"$f":"B5-B22","v":9.9960995258878214}]
["Interval Upper Limit",{"$f":"B5+B22","v":10.003900474112179}]

{"sheet":"ExponentialWS","index":31,"n_rows":8,"n_cols":2,"rows_kept":8,"cut":false,"hidden":false,"merged":[[2,0,2,1],[6,0,6,1]]}
["Exponential Probability"]
[]
["Data"]
["Mean",20]
["X Value",0.1]
[]
["Results"]
["P(<=X)",{"$f":"EXPONDIST(B5,B4,TRUE)","v":0.8646647167633873}]

{"sheet":"NormalWS","index":32,"n_rows":38,"n_cols":2,"rows_kept":38,"cut":false,"hidden":false,"merged":[[33,0,33,1],[16,0,16,1],[2,0,2,1],[19,0,19,1],[6,0,6,1],[11,0,11,1],[28,0,28,1]]}
["Normal Probabilities"]
[]
["Common Data"]
["Mean",7]
["Standard Deviation",2]
[]
["Probability for X <="]
["X Value",7]
["Z Value",{"$f":"STANDARDIZE(B8,B4,B5)","v":0}]
[{"$f":"\"P(X<=\"&B8&\")\"","v":"P(X<=7)"},{"$f":"NORMDIST(B8,B4,B5,TRUE)","v":0.5}]
[]
["Probability for X >"]
["X Value",9]
["Z Value",{"$f":"STANDARDIZE(B13,B4,B5)","v":1}]
[{"$f":"\"P(X>\"&B13&\")\"","v":"P(X>9)"},{"$f":"1-NORMDIST(B13,B4,B5,TRUE)","v":0.15865525393145696}]
[]
[{"$f":"\"Probability for X<\"&B8&\" or X >\"&B13","v":"Probability for X<7 or X >9"}]
[{"$f":"\"P(X<\"&B8&\" or X >\"&B13 & \")\"","v":"P(X<7 or X >9)"},{"$f":"B10+B15","v":0.65865525393145696}]
[]
["Probability for a Range"]
["From X Value",5]
["To X Value",9]
[{"$f":"\"Z Value for \" &B21","v":"Z Value for 5"},{"$f":"STANDARDIZE(B21,B4,B5)","v":-1}]
[{"$f":"\"Z Value for \" & B22","v":"Z Value for 9"},{"$f":"STANDARDIZE(B22,B4,B5)","v":1}]
[{"$f":"\"P(X<=\"&B21&\")\"","v":"P(X<=5)"},{"$f":"NORMDIST(B21,B4,B5,TRUE)","v":0.15865525393145699}]
[{"$f":"\"P(X<=\"&B22&\")\"","v":"P(X<=9)"},{"$f":"NORMDIST(B22,B4,B5,TRUE)","v":0.84134474606854304}]
[{"$f":"\"P(\"&B21&\"<=X<=\"&B22&\")\"","v":"P(5<=X<=9)"},{"$f":"ABS(B26-B25)","v":0.68268949213708607}]
[]
["Find X and Z Given Cum. Pctage."]
["Cumulative Percentage",0.1]
["Z Value",{"$f":"NORMSINV(B30)","v":-1.2815515655446006}]
["X Value",{"$f":"NORMINV(B30,B4,B5)","v":4.4368968689107984}]
[]
["Find X Values Given a Percentage"]
["Percentage",0.95]
["Z Value",{"$f":"NORMSINV((1 - B35)/2)","v":-1.9599639845400536}]
["Lower X Value",{"$f":"B4 + B36 * B5","v":3.0800720309198928}]
["Upper X Value",{"$f":"B4 - B36 * B5","v":10.919927969080106}]

{"sheet":"HypergeoWS","index":33,"n_rows":11,"n_cols":3,"rows_kept":11,"cut":false,"hidden":false,"merged":[[2,0,2,1]]}
["Hypergeometric Probabilities"]
[]
["Data"]
["Sample size",1]
["No. of events of interest in population",1]
["Population size",2]
[]
["Hypergeometric Probabilities Table"]
[null,"X","P(X)"]
[null,0,{"$f":"HYPGEOMDIST(B10,$B$4,$B$5,$B$6)","v":0.5}]
[null,1,{"$f":"HYPGEOMDIST(B11,$B$4,$B$5,$B$6)","v":0.5}]

{"sheet":"PoissonWS","index":34,"n_rows":28,"n_cols":7,"rows_kept":28,"cut":false,"hidden":false,"merged":[[2,0,2,4]]}
["Poisson Probabilities"]
[]
["Data"]
["Mean/Expected number of events of interest:",null,null,null,3]
[]
["Poisson Probabilities Table"]
[null,"X","P(X)","P(<=X)","P(<X)","P(>X)","P(>=X)"]
[null,0,{"$f":"POISSON(B8,$E$4,FALSE)","v":4.9787068367863944E-2},{"$f":"POISSON(B8,$E$4,TRUE)","v":4.9787068367863944E-2},{"$f":"D8-C8","v":0},{"$f":"1-D8","v":0.95021293163213605},{"$f":"1-E8","v":1}]
[null,1,0.14936120510359185,{"$f":"POISSON(B9,$E$4,TRUE)","v":0.19914827347145578},{"$f":"D9-C9","v":4.9787068367863924E-2},{"$f":"1-D9","v":0.80085172652854419},0.95021293163213605]
[null,2,0.22404180765538775,0.42319008112684342,0.19914827347145567,0.57680991887315658,0.80085172652854431]
[null,3,0.22404180765538778,0.64723188878223126,0.42319008112684348,0.35276811121776874,0.57680991887315658]
[null,4,0.16803135574154085,0.81526324452377208,0.64723188878223126,0.18473675547622792,0.35276811121776874]
[null,5,0.10081881344492449,0.91608205796869657,0.81526324452377208,8.3917942031303427E-2,0.18473675547622792]
[null,6,5.0409406722462261E-2,0.96649146469115887,0.91608205796869657,3.3508535308841125E-2,8.3917942031303427E-2]
[null,7,2.1604031452483807E-2,0.98809549614364256,0.96649146469115876,1.190450385635744E-2,3.3508535308841236E-2]
[null,8,8.1015117946814375E-3,0.996197007938324,0.98809549614364256,3.8029920616760027E-3,1.190450385635744E-2]
[null,9,2.7005039315604771E-3,0.99889751186988451,0.996197007938324,1.1024881301154865E-3,3.8029920616760027E-3]
[null,10,8.1015117946814244E-4,0.99970766304935266,0.99889751186988451,2.9233695064734277E-4,1.1024881301154865E-3]
[null,11,2.2095032167312987E-4,0.99992861337102579,0.99970766304935266,7.1386628974212663E-5,2.9233695064734277E-4]
[null,12,5.5237580418282596E-5,0.99998385095144404,0.99992861337102579,1.614904855595789E-5,7.1386628974212663E-5]
[null,13,1.2747133942680586E-5,0.99999659808538677,0.99998385095144404,3.4019146132324707E-6,1.614904855595789E-5]
[null,14,2.7315287020029766E-6,0.99999932961408877,0.99999659808538677,6.7038591122781099E-7,3.4019146132324707E-6]
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{"sheet":"BinomialWS","index":35,"n_rows":14,"n_cols":7,"rows_kept":14,"cut":false,"hidden":false,"merged":[[2,0,2,1],[6,0,6,1]]}
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[]
["Data"]
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[]
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[]
["Binomial Probabilities Table"]
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{"sheet":"nuLRWS","index":36,"n_rows":4,"n_cols":7,"rows_kept":4,"cut":false,"hidden":false,"merged":[]}
["Logistic Regression",null,null,null,null,null,"Y"]
[]
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{"sheet":"nuDescSummaryWS","index":37,"n_rows":16,"n_cols":2,"rows_kept":16,"cut":false,"hidden":false,"merged":[]}
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[]
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["Skewness",{"$f":"SKEW(E:E)","v":{"$error":"#DIV/0!"}}]
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{"sheet":"nuATFWORWS","index":38,"n_rows":24,"n_cols":7,"rows_kept":24,"cut":false,"hidden":false,"merged":[[23,3,23,5]]}
["ANOVA: Two-Factor Without Replication"]
[]
["SUMMARY","Count","Sum","Average","Variance"]
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[]
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["Restaurant C",6,546,91,33.200000000000003]
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[]
[]
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[]
["Total",null,{"$f":"SUM(C19:C21)","v":0}]
[null,null,null,"Level of significance",null,null,0.05]

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[null,null,null,null,null,null,null,null,null,null,"t Critical Value",{"$f":"_xlfn.T.INV.2T(1-L8, B13)","v":{"$error":"#NUM!"}}]
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[null,"df","SS","MS","F","Significance F",null,null,null,null,"Half Width b1",{"$f":"L$9 * C18","v":{"$error":"#NUM!"}}]
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["Residual",{"$f":"M5","v":0},{"$f":"M6","v":0},{"$f":"C13/B13","v":{"$error":"#DIV/0!"}}]
["Total",{"$f":"B8-1","v":-1},{"$f":"C12+C13","v":0}]
[]
[null,"Coefficients","Standard Error","t Stat","P-value",{"$f":"\"Lower \" & TEXT(L8, \"##%\")","v":"Lower 95%"},{"$f":"\"Upper \" & TEXT(L8, \"##%\")","v":"Upper 95%"},{"$f":"F16","v":"Lower 95%"},"Upper 95%"]
["Intercept",{"$f":"N2","v":0},{"$f":"N3","v":0},{"$f":"B17/C17","v":{"$error":"#DIV/0!"}},{"$f":"_xlfn.T.DIST.2T(ABS(D17), B$13)","v":{"$error":"#DIV/0!"}},{"$f":"B17-L10","v":{"$error":"#NUM!"}},{"$f":"B17+L10","v":{"$error":"#NUM!"}},{"$error":"#NUM!"},{"$error":"#NUM!"}]
[null,{"$f":"M2","v":0},{"$f":"M3","v":0},{"$f":"B18/C18","v":{"$error":"#DIV/0!"}},{"$f":"_xlfn.T.DIST.2T(ABS(D18), B$13)","v":{"$error":"#DIV/0!"}},{"$f":"B18-L11","v":{"$error":"#NUM!"}},{"$f":"B18+L11","v":{"$error":"#NUM!"}},{"$error":"#NUM!"},{"$error":"#NUM!"}]
[null,{"$f":"L2","v":0},{"$f":"L3","v":0},{"$f":"B19/C19","v":{"$error":"#DIV/0!"}},{"$error":"#DIV/0!"},{"$f":"B19-L12","v":{"$error":"#NUM!"}},{"$f":"B19+L12","v":{"$error":"#NUM!"}},{"$error":"#NUM!"},{"$error":"#NUM!"}]

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[5,3,6]
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{"sheet":"nuSLRWS","index":41,"n_rows":18,"n_cols":12,"rows_kept":18,"cut":false,"hidden":false,"merged":[[0,10,0,12]]}
["Simple Linear Regression",null,null,null,null,null,null,null,null,null,"Calculations"]
[null,null,null,null,null,null,null,null,null,null,"b1, b0 Coefficients"]
["Regression Statistics",null,null,null,null,null,null,null,null,null,"b1, b0 Standard Error"]
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["R Square",{"$f":"L4","v":0},null,null,null,null,null,null,null,null,"F, Residual df"]
["Adjusted R Square",{"$f":"1-(B14/B13)*(C13/C14)","v":{"$error":"#DIV/0!"}},null,null,null,null,null,null,null,null,"Regression SS, Residual SS"]
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["Observations",{"$f":"COUNT(#REF!)","v":0},null,null,null,null,null,null,null,null,"Confidence level",0.95]
[null,null,null,null,null,null,null,null,null,null,"t Critical Value",{"$f":"_xlfn.T.INV.2T(1-L8,B13)","v":{"$error":"#NUM!"}}]
["ANOVA",null,null,null,null,null,null,null,null,null,"Half Width b0",{"$f":"L9*C17","v":{"$error":"#NUM!"}}]
[null,"df","SS","MS","F","Significance F",null,null,null,null,"Half Width b1",{"$f":"L9*C18","v":{"$error":"#NUM!"}}]
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["Residual",{"$f":"M5","v":0},{"$f":"M6","v":0},{"$f":"C13/B13","v":{"$error":"#DIV/0!"}}]
["Total",{"$f":"B12+B13","v":1},{"$f":"C12+C13","v":0}]
[]
[null,"Coefficients","Standard Error","t Stat","P-value",{"$f":"\"Lower \" & L8*100 & \"%\"","v":"Lower 95%"},{"$f":"\"Upper \" & L8*100 & \"%\"","v":"Upper 95%"},{"$f":"F16","v":"Lower 95%"},"Upper 95%"]
["Intercept",{"$f":"M2","v":0},{"$f":"M3","v":0},{"$f":"B17/C17","v":{"$error":"#DIV/0!"}},{"$f":"_xlfn.T.DIST.2T(ABS(D17), B13)","v":{"$error":"#DIV/0!"}},{"$f":"B17-L10","v":{"$error":"#NUM!"}},{"$f":"B17+L10","v":{"$error":"#NUM!"}},{"$error":"#NUM!"},{"$error":"#NUM!"}]
[null,{"$f":"L2","v":0},{"$f":"L3","v":0},{"$f":"B18/C18","v":{"$error":"#DIV/0!"}},{"$f":"_xlfn.T.DIST.2T(ABS(D18), B13)","v":{"$error":"#DIV/0!"}},{"$f":"B18-L11","v":{"$error":"#NUM!"}},{"$f":"B18+L11","v":{"$error":"#NUM!"}},{"$error":"#NUM!"},{"$error":"#NUM!"}]

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["Best Subset Analysis"]
[]
["Intermediate Calculations"]
["R2T"]
["1 - R2T",{"$f":"1-B4","v":1}]
["n"]
["T",0]
["n - T",{"$f":"B6-B7","v":0}]
[]
["Model","Cp","k+1","R Square","Adj. R Square","Std. Error"]
["X1",{"$f":"((1-D11)*($B$8))/$B$5-$B$6+2*(C11)","v":0}]

{"sheet":"nuATFRWS","index":43,"n_rows":31,"n_cols":7,"rows_kept":31,"cut":false,"hidden":false,"merged":[[30,3,30,5]]}
["Anova: Two-Factor With Replication"]
[]
["SUMMARY","CF1","CF2","CF3","CF4","Total"]
["RF1"]
["Count",null,{"$f":"B5","v":0},{"$f":"B5","v":0},{"$f":"B5","v":0},{"$f":"SUM(B5:E5)","v":0}]
["Sum",null,null,null,null,{"$f":"SUM(B6:E6)","v":0}]
["Average",null,null,null,null,{"$f":"AVERAGE(B7:E7)","v":{"$error":"#DIV/0!"}}]
["Variance"]
[]
["RF2"]
["Count",null,{"$f":"B11","v":0},{"$f":"B11","v":0},{"$f":"B11","v":0},{"$f":"SUM(B11:E11)","v":0}]
["Sum",null,null,null,null,{"$f":"SUM(B12:E12)","v":0}]
["Average",null,null,null,null,{"$f":"AVERAGE(B13:E13)","v":{"$error":"#DIV/0!"}}]
["Variance"]
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["Total"]
["Count",null,"x","x","x"]
["Sum"]
["Average"]
["Variance"]
[]
[]
["ANOVA"]
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["Sample",null,1,{"$f":"B25/C25","v":0},{"$f":"D25/D$28","v":{"$error":"#DIV/0!"}},{"$f":"_xlfn.F.DIST.RT(E25,C25,C$28)","v":{"$error":"#DIV/0!"}},{"$f":"_xlfn.F.INV.RT(G$31,C25,C$28)","v":{"$error":"#NUM!"}}]
["Columns",null,{"$f":"COUNTA(3:3)-3","v":3},{"$f":"B26/C26","v":0},{"$f":"D26/D$28","v":{"$error":"#DIV/0!"}},{"$f":"_xlfn.F.DIST.RT(E26,C26,C$28)","v":{"$error":"#DIV/0!"}},{"$f":"_xlfn.F.INV.RT(G$31,C26,C$28)","v":{"$error":"#NUM!"}}]
["Interaction",{"$f":"B30-B25-B26-B28","v":0},{"$f":"C25*C26","v":3},{"$f":"B27/C27","v":0},{"$f":"D27/D$28","v":{"$error":"#DIV/0!"}},{"$error":"#DIV/0!"},{"$error":"#NUM!"}]
["Within",null,{"$f":"(C25+1)*(C26+1)*(B5-1)","v":-8},{"$f":"B28/C28","v":0}]
[]
["Total",null,{"$f":"SUM(C25:C28)","v":-1}]
[null,null,null,"Level of significance",null,null,0.05]

{"sheet":"nuASFWS","index":44,"n_rows":17,"n_cols":10,"rows_kept":17,"cut":false,"hidden":false,"merged":[[0,8,0,9],[16,3,16,5]]}
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[null,null,null,null,null,null,null,null,"c"]
["SUMMARY",null,null,null,null,null,null,null,"n",{"$f":"SUM(B5:B8)","v":0}]
["Groups","Count","Sum","Average","Variance"]
["Group 1"]
["Group 2"]
["Group 3"]
["Group 4"]
[]
[]
["ANOVA"]
["Source of Variation","SS","df","MS","F","P-value","F crit"]
["Between Groups",null,{"$f":"J2-1","v":-1},{"$f":"B13/C13","v":0},{"$f":"D13/D14","v":{"$error":"#DIV/0!"}},{"$f":"_xlfn.F.DIST.RT(E13,C13,C14)","v":{"$error":"#DIV/0!"}},{"$f":"_xlfn.F.INV.RT(G17,C13,C14)","v":{"$error":"#NUM!"}}]
["Within Groups",{"$f":"B16-B13","v":0},{"$f":"J3-J2","v":0},{"$f":"B14/C14","v":{"$error":"#DIV/0!"}}]
[]
["Total",null,{"$f":"C13+C14","v":-1}]
[null,null,null,"Level of significance",null,null,0.05]

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["Data"]
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[null,{"$f":"(COUNTIF($A$2:$A$5,$A4)-1)*0.025+1-(COUNTIF($A$2:$A3,$A4)*0.025)","v":0.97499999999999998},{"$f":"AVERAGE(A:A)","v":{"$error":"#DIV/0!"}},0.7,null,null,null,{"$f":"IF(H3=INT(H3),\"Rule 1 applies\", IF(H3=CEILING(H3,0.5),\"Rule 2 applies\", \"Rule 3 applies\"))","v":"Rule 3 applies"}]
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[null,{"$f":"(COUNTIF($A$2:$A$18,$A7)-1)*0.025+1-(COUNTIF($A$2:$A6,$A7)*0.025)","v":0.97499999999999998},{"$f":"MEDIAN(A:A)","v":{"$error":"#NUM!"}},0.7,null,null,"first quartile:",{"$f":"IF(H4=\"Rule 2 applies\",(H6+I6)/2,H6)","v":{"$error":"#NUM!"}}]
[null,{"$f":"(COUNTIF($A$2:$A$18,$A8)-1)*0.025+1-(COUNTIF($A$2:$A7,$A8)*0.025)","v":0.97499999999999998},"1st Quartile",null,null,null,"Initial third quartile rank",{"$f":"(3*(COUNT(A:A)+1))/4","v":0.75}]
[null,{"$f":"(COUNTIF($A$2:$A$18,$A9)-1)*0.025+1-(COUNTIF($A$2:$A8,$A9)*0.025)","v":0.97499999999999998},{"$f":"H7","v":{"$error":"#NUM!"}},0.95,null,null,null,{"$f":"IF(H8=INT(H8),\"Rule 1 applies\", IF(H8=CEILING(H8,0.5),\"Rule 2 applies\", \"Rule 3 applies\"))","v":"Rule 3 applies"}]
[null,{"$f":"(COUNTIF($A$2:$A$18,$A10)-1)*0.025+1-(COUNTIF($A$2:$A9,$A10)*0.025)","v":0.97499999999999998},{"$f":"H7","v":{"$error":"#NUM!"}},0.7,null,null,{"$f":"IF(H9=\"Rule 2 applies\", \"average these ranks:\", \"use rank:\")","v":"use rank:"},{"$f":"IF(H9=\"Rule 2 applies\",FLOOR(H8,1),ROUND(H8,0))","v":1},{"$f":"IF(H9=\"Rule 2 applies\", CEILING(H8,1), \"\")","v":""}]
[null,{"$f":"(COUNTIF($A$2:$A$18,$A11)-1)*0.025+1-(COUNTIF($A$2:$A10,$A11)*0.025)","v":0.97499999999999998},"3rd Quartile",null,null,null,{"$f":"IF(H9=\"Rule 2 applies\", \"average these values:\", \"value of rank:\")","v":"value of rank:"},{"$f":"SMALL(A:A,H10)","v":{"$error":"#NUM!"}},{"$f":"IF(H9=\"Rule 2 applies\",SMALL(A:A,I10),\"\")","v":""}]
[null,{"$f":"(COUNTIF($A$2:$A$18,$A12)-1)*0.025+1-(COUNTIF($A$2:$A11,$A12)*0.025)","v":0.97499999999999998},{"$f":"H12","v":{"$error":"#NUM!"}},0.95,null,null,"third quartile:",{"$f":"IF(H9=\"Rule 2 applies\",(H11+I11)/2,H11)","v":{"$error":"#NUM!"}}]
[null,{"$f":"(COUNTIF($A$2:$A$18,$A13)-1)*0.025+1-(COUNTIF($A$2:$A12,$A13)*0.025)","v":0.97499999999999998},{"$f":"H12","v":{"$error":"#NUM!"}},0.7]
[null,{"$f":"(COUNTIF($A$2:$A$18,$A14)-1)*0.025+1-(COUNTIF($A$2:$A13,$A14)*0.025)","v":0.97499999999999998},"Std. Deviation"]
[null,{"$f":"(COUNTIF($A$2:$A$18,$A15)-1)*0.025+1-(COUNTIF($A$2:$A14,$A15)*0.025)","v":0.97499999999999998},{"$f":"_xlfn.STDEV.S(A:A)","v":{"$error":"#DIV/0!"}},{"$f":"C15*2","v":{"$error":"#DIV/0!"}},{"$f":"C15*3","v":{"$error":"#DIV/0!"}}]
[null,{"$f":"(COUNTIF($A$2:$A$18,$A16)-1)*0.025+1-(COUNTIF($A$2:$A15,$A16)*0.025)","v":0.97499999999999998},"1 Std. Dev"]
[null,{"$f":"(COUNTIF($A$2:$A$18,$A17)-1)*0.025+1-(COUNTIF($A$2:$A16,$A17)*0.025)","v":0.97499999999999998},{"$f":"$C$3-$C$15","v":{"$error":"#DIV/0!"}},0.9]
[null,{"$f":"(COUNTIF($A$2:$A$18,$A18)-1)*0.025+1-(COUNTIF($A$2:$A17,$A18)*0.025)","v":0.97499999999999998},{"$f":"$C$3+$C$15","v":{"$error":"#DIV/0!"}},0.9]
[null,null,"2 Std Dev."]
[null,null,{"$f":"$C$3-$D$15","v":{"$error":"#DIV/0!"}},0.8]
[null,null,{"$f":"$C$3+$D$15","v":{"$error":"#DIV/0!"}},0.8]
[null,null,"3 Std Dev"]
[null,null,{"$f":"$C$3-$E$15","v":{"$error":"#DIV/0!"}},0.7]
[null,null,{"$f":"$C$3+$E$15","v":{"$error":"#DIV/0!"}},0.7]
[]
[null,null,null,null,"Summary"]
[null,null,null,null,"Mean",{"$f":"C3","v":{"$error":"#DIV/0!"}}]
[null,null,null,null,"Median",{"$f":"C6","v":{"$error":"#NUM!"}}]
[null,null,null,null,"1st Quartile",{"$f":"C9","v":{"$error":"#NUM!"}}]
[null,null,null,null,"3rd Quartile",{"$f":"C12","v":{"$error":"#NUM!"}}]
[null,null,null,null,"Std. Deviation",{"$f":"C15","v":{"$error":"#DIV/0!"}}]

{"sheet":"nuCIPVWS","index":46,"n_rows":23,"n_cols":2,"rows_kept":23,"cut":false,"hidden":false,"merged":[[2,0,2,1],[7,0,7,1],[14,0,14,1]]}
["Confidence Interval Estimate for the Population Variance"]
[]
["Data"]
["Sample Size",2]
["Sample Standard Deviation",1]
["Confidence Level",0.95]
[]
["Intermediate Calculations"]
["Degrees of Freedom",{"$f":"B4-1","v":1}]
["Sum of Squares",{"$f":"B9*B5^2","v":1}]
["Single Tail Area",{"$f":"(1-B6)/2","v":2.5000000000000022E-2}]
["Lower Chi-Square Value",{"$f":"_xlfn.CHISQ.INV.RT(1-B11, B9)","v":9.8206911717525812E-4}]
["Upper Chi-Square Value",{"$f":"_xlfn.CHISQ.INV.RT(B11, B9)","v":5.0238861873148863}]
[]
["Results"]
["Interval Lower Limit for Variance",{"$f":"B10/B13","v":0.19904909520541297}]
["Interval Upper Limit for Variance",{"$f":"B10/B12","v":1018.2582697196677}]
[]
["Interval Lower Limit for Standard Deviation",{"$f":"SQRT(B16)","v":0.44614918492070899}]
["Interval Upper Limit for Standard Deviation",{"$f":"SQRT(B17)","v":31.910159349643926}]
[]
["Assumption:"]
["Population from which sample was drawn has an approximate normal distribution."]

{"sheet":"nuCSTVWS","index":47,"n_rows":28,"n_cols":2,"rows_kept":28,"cut":false,"hidden":false,"merged":[[8,0,8,1]]}
["Chi-Square Test of Hypothesis for the Variance"]
[]
["Data"]
["Null Hypothesis                        s^2=",1]
["Level of Significance",0.05]
["Sample Size",10]
["Sample Standard Deviation",2]
[]
["Intermediate Calculations"]
["Degrees of Freedom",{"$f":"B6-1","v":9}]
["Half Area",{"$f":"B5/2","v":2.5000000000000001E-2}]
["Chi-Square Statistic",{"$f":"B10*B7^2/B4","v":36}]
[]
["Two-Tail Test"]
["Lower Critical Value",{"$f":"_xlfn.CHISQ.INV.RT(1-B11, B10)","v":2.7003894999803584}]
["Upper Critical Value",{"$f":"_xlfn.CHISQ.INV.RT(B11, B10)","v":19.022767798641635}]
["p-Value",{"$f":"IF(B12<_xlfn.CHISQ.INV.RT(0.5, B10), 1-_xlfn.CHISQ.DIST.RT(B12, B10), _xlfn.CHISQ.DIST.RT(B12, B10))","v":3.9646587980428506E-5}]
[{"$f":"IF(B17<$B$5/2,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Reject the null hypothesis"}]
[]
["Lower-Tail Test"]
["Lower Critical Value",{"$f":"_xlfn.CHISQ.INV.RT(1-B5, B10)","v":3.3251128430668162}]
["p-Value",{"$f":"1-_xlfn.CHISQ.DIST.RT(B12, B10)","v":0.99996035341201961}]
[{"$f":"IF(B22<$B$5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]
[]
["Upper-Tail Test"]
["Upper Critical Value",{"$f":"_xlfn.CHISQ.INV.RT(B5, B10)","v":16.918977604620451}]
["p-Value",{"$f":"_xlfn.CHISQ.DIST.RT(B12,B10)","v":3.9646587980428506E-5}]
[{"$f":"IF(B27<$B$5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Reject the null hypothesis"}]

{"sheet":"nuCovarianceWS","index":48,"n_rows":24,"n_cols":9,"rows_kept":24,"cut":false,"hidden":false,"merged":[[8,0,8,1],[19,0,19,1]]}
["Covariance Analysis"]
[]
["Probabilities & Outcomes:","P","X","Y"]
[]
[]
[]
["Weight Assigned to X",0.5]
[]
["Statistics"]
["E(X)",{"$f":"SUMPRODUCT(B4:B5,C4:C5)","v":0},null,null,"Calculations Area"]
["E(Y)",{"$f":"SUMPRODUCT(B4:B5,D4:D5)","v":0},null,null,"For variance and standard deviation:",null,null,null,"For covariance:"]
["Variance(X)",{"$f":"SUMPRODUCT(B4:B5,G13:G14)","v":0},null,null,"X-mu","Y-mu","(X-mu)^2","(Y-mu)^2","(X-mu)(Y-mu)"]
["Standard Deviation(X)",{"$f":"SQRT(B12)","v":0},null,null,{"$f":"C4-$B$10","v":0},{"$f":"D4-$B$11","v":0},{"$f":"E13^2","v":0},{"$f":"F13^2","v":0},{"$f":"E13*F13","v":0}]
["Variance(Y)",{"$f":"SUMPRODUCT(B4:B5,H13:H14)","v":0},null,null,{"$f":"C5-$B$10","v":0},{"$f":"D5-$B$11","v":0},{"$f":"E14^2","v":0},{"$f":"F14^2","v":0},{"$f":"E14*F14","v":0}]
["Standard Deviation(Y)",{"$f":"SQRT(B14)","v":0}]
["Covariance(XY)",{"$f":"SUMPRODUCT(B4:B5,I13:I14)","v":0}]
["Variance(X+Y)",{"$f":"B12+B14+2*B16","v":0}]
["Standard Deviation(X+Y)",{"$f":"SQRT(B17)","v":0}]
[]
["Portfolio Management"]
["Weight Assigned to X",{"$f":"B7","v":0.5}]
["Weight Assigned  to Y",{"$f":"1-B21","v":0.5}]
["Portfolio Expected Return",{"$f":"B21*B10+B22*B11","v":0}]
["Portfolio Risk",{"$f":"SQRT(B21^2*B12+B22^2*B14+2*B21*B22*B16)","v":0}]

{"sheet":"RXChartWS","index":49,"n_rows":30,"n_cols":7,"rows_kept":30,"cut":false,"hidden":false,"merged":[[1,3,1,6],[2,0,2,1],[5,0,5,1],[10,0,10,1],[20,0,20,1]]}
["Control Charts"]
[null,null,null,"Control Chart Factors Table"]
["Data",null,null,"Subgroup size","D3","D4","A2"]
["Sample/Subgroup Size",5,null,2,0,3.2669999999999999,1.88]
[null,null,null,3,0,2.5750000000000002,1.0229999999999999]
["R Chart Intermediate Calculations",null,null,4,0,2.282,0.72899999999999998]
["RBar",null,null,5,0,2.1139999999999999,0.57699999999999996]
["D3 Factor",{"$f":"VLOOKUP($B$4,$D$4:$G$28,2)","v":0},null,6,0,2.004,0.48299999999999998]
["D4 Factor",{"$f":"VLOOKUP($B$4,$D$4:$G$28,3)","v":2.1139999999999999},null,7,7.5999999999999998E-2,1.9239999999999999,0.41899999999999998]
[null,null,null,8,0.13600000000000001,1.8640000000000001,0.373]
["R Chart Control Limits",null,null,9,0.184,1.8160000000000001,0.33700000000000002]
["Lower Control Limit",{"$f":"B8*B7","v":0},null,10,0.223,1.7769999999999999,0.308]
["Center",{"$f":"B7","v":0},null,11,0.25600000000000001,1.744,0.28499999999999998]
["Upper Control Limit",{"$f":"B9*B7","v":0},null,12,0.28299999999999997,1.7170000000000001,0.26600000000000001]
[null,null,null,13,0.307,1.6930000000000001,0.249]
["XBar Chart Intemediate Calculations",null,null,14,0.32800000000000001,1.6719999999999999,0.23499999999999999]
["Average of Subgroup Averages",null,null,15,0.34699999999999998,1.653,0.223]
["A2 Factor",{"$f":"VLOOKUP($B$4,$D$4:$G$28,4)","v":0.57699999999999996},null,16,0.36299999999999999,1.637,0.21199999999999999]
["A2 Factor * RBar",{"$f":"B18*B7","v":0},null,17,0.378,1.6220000000000001,0.20300000000000001]
[null,null,null,18,0.39100000000000001,1.609,0.19400000000000001]
["XBar Chart Control Limits",null,null,19,0.40400000000000003,1.5960000000000001,0.187]
["Lower Control Limit",{"$f":"B17-B19","v":0},null,20,0.41499999999999998,1.585,0.18]
["Center",{"$f":"B17","v":0},null,21,0.42499999999999999,1.575,0.17299999999999999]
["Upper Control Limit",{"$f":"B17+B19","v":0},null,22,0.435,1.5649999999999999,0.16700000000000001]
[null,null,null,23,0.443,1.5569999999999999,0.16200000000000001]
[null,null,null,24,0.45200000000000001,1.548,0.157]
[null,null,null,25,0.45900000000000002,1.5409999999999999,0.153]
[null,null,null,26,{"$f":"D30","v":"Factor value not available. Possible error in sample/subgroup size."},{"$f":"D30","v":"Factor value not available. Possible error in sample/subgroup size."},{"$f":"D30","v":"Factor value not available. Possible error in sample/subgroup size."}]
[]
[null,null,null,"Factor value not available. Possible error in sample/subgroup size."]

{"sheet":"pChartWS","index":50,"n_rows":14,"n_cols":2,"rows_kept":14,"cut":false,"hidden":false,"merged":[[2,0,2,1]]}
["p Chart Summary"]
[]
["Intermediate Calculations"]
["Sum of Subgroup Sizes"]
["Number of Subgroups Taken"]
["Average Sample/Subgroup Size",{"$f":"B4/B5","v":{"$error":"#DIV/0!"}}]
["Average Proportion of Nonconforming Items"]
["Three Standard Deviations",{"$f":"3*SQRT(B7*(1-B7)/B6)","v":{"$error":"#DIV/0!"}}]
["Preliminary Lower Control Limit",{"$f":"B7-B8","v":{"$error":"#DIV/0!"}}]
[]
["p Chart Control Limits"]
["Lower Control Limit",{"$f":"IF(B9 > 0, B9, 0)","v":{"$error":"#DIV/0!"}}]
["Center",{"$f":"B7","v":0}]
["Upper Control Limit",{"$f":"B7+B8","v":{"$error":"#DIV/0!"}}]

{"sheet":"cChartWS","index":51,"n_rows":12,"n_cols":2,"rows_kept":12,"cut":false,"hidden":false,"merged":[[2,0,2,1]]}
["c Chart Summary"]
[]
["Intermediate Calculations"]
["Sum of Nonconformities","=SUM(cChartData!B:B)"]
["Number of Units Sampled","=COUNT(cChartData!B:B)"]
["Cbar",{"$f":"B4/B5","v":{"$error":"#VALUE!"}}]
["Preliminary Lower Control Limit",{"$f":"B6-3*SQRT(B6)","v":{"$error":"#VALUE!"}}]
[]
["c Chart Control Limits"]
["Lower Control Limit",{"$f":"IF(B7 > 0, B7, 0)","v":{"$error":"#VALUE!"}}]
["Center",{"$f":"B6","v":{"$error":"#VALUE!"}}]
["Upper Control Limit",{"$f":"B6+3*SQRT(B6)","v":{"$error":"#VALUE!"}}]

{"sheet":"nuTSPTWS","index":52,"n_rows":29,"n_cols":5,"rows_kept":29,"cut":false,"hidden":false,"merged":[[14,3,14,4],[23,0,23,1],[25,0,25,1],[28,0,28,1],[2,0,2,1],[6,0,6,1],[14,0,14,1],[18,0,18,1],[20,0,20,1]]}
["Paired t Test"]
[]
["Data"]
["Hypothesized Mean Difference",0]
["Level of significance",0.05]
[]
["Intermediate Calculations"]
["Sample Size",10]
["DBar",2]
["Degrees of Freedom",{"$f":"B8-1","v":9}]
["SD",2]
["Standard Error",{"$f":"B11/SQRT(B8)","v":0.63245553203367588}]
["t Test Statistic",{"$f":"(B9-B4)/B12","v":3.1622776601683791}]
[]
["Two-Tail Test",null,null,"TDIST Calculations"]
["Lower Critical Value",{"$f":"-_xlfn.T.INV.2T(B5, B10)","v":-2.2621571627982053},null,"T.DIST.RT",{"$f":"_xlfn.T.DIST.RT(ABS(B13),B10)","v":5.75399258297183E-3}]
["Upper Critical Value",{"$f":"_xlfn.T.INV.2T(B5, B10)","v":2.2621571627982053},null,"1-T.DIST.RT",{"$f":"1-E16","v":0.99424600741702818}]
["p-Value",{"$f":"_xlfn.T.DIST.2T(ABS(B13), B10)","v":1.150798516594366E-2}]
[{"$f":"IF(B18 < B5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Reject the null hypothesis"}]
[]
["Lower-Tail Test"]
["Lower Critical Value",{"$f":"-_xlfn.T.INV.2T(2*B5, B10)","v":-1.8331129326562374}]
["p-Value",{"$f":"IF(B13<0, E16, E17)","v":0.99424600741702818}]
[{"$f":"IF(B23 < B5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]
[]
["Upper-Tail Test"]
["Upper Critical Value",{"$f":"_xlfn.T.INV.2T(2*B5, B10)","v":1.8331129326562374}]
["p-Value",{"$f":"IF(B13<0, E17, E16)","v":5.75399258297183E-3}]
[{"$f":"IF(B28 < B5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Reject the null hypothesis"}]

{"sheet":"nuTSTTSVWS","index":53,"n_rows":38,"n_cols":5,"rows_kept":38,"cut":false,"hidden":false,"merged":[[2,0,2,1],[14,0,14,1],[14,3,14,4]]}
["Separate-Variances t Test for the Difference Between Two Means"]
["(assumes unequal population variances)"]
["Data"]
["Hypothesized Difference",0]
["Level of Significance",0.05]
["Population 1 Sample"]
["Sample Size",10]
["Sample Mean",10]
["Sample Standard Deviation",8]
["Population 2 Sample"]
["Sample Size",10]
["Sample Mean",18]
["Sample Standard Deviation",10]
[]
["Intermediate Calculations",null,null,"Calculations Area"]
["Numerator of Degrees of Freedom",{"$f":"(E18+E19)^2","v":268.95999999999998},null,"Pop. 1 Sample Variance",{"$f":"B9^2","v":64}]
["Denominator of Degrees of Freedom",{"$f":"(E18^2)/(B7-1)+(E19^2)/(B11-1)","v":15.662222222222223},null,"Pop. 2 Sample Variance",{"$f":"B13^2","v":100}]
["Total Degrees of Freedom",{"$f":"B16/B17","v":17.172531214528941},null,"Pop. 1 Sample Var./Sample Size",{"$f":"E16/B7","v":6.4}]
["Degrees of Freedom",{"$f":"INT(B18)","v":17},null,"Pop. 2 Sample Var./Sample Size",{"$f":"E17/B11","v":10}]
["Standard Error",{"$f":"SQRT(E18+E19)","v":4.0496913462633168},null,"For one-tailed tests:"]
["Difference in Sample Means",{"$f":"B8-B12","v":-8},null,"T.DIST.RT value",{"$f":"_xlfn.T.DIST.RT(ABS(B22),B19)","v":3.2340349941363422E-2}]
["Separate-Variance t Test Statistic",{"$f":"(B21-B4)/B20","v":-1.9754591932991794},null,"1-T.DIST.RT value",{"$f":"1-E21","v":0.96765965005863652}]
[]
["Two-Tail Test"]
["Lower Critical Value",{"$f":"-(_xlfn.T.INV.2T(B5,B19))","v":-2.109815577833317}]
["Upper Critical Value",{"$f":"_xlfn.T.INV.2T(B5,B19)","v":2.109815577833317}]
["p-Value",{"$f":"_xlfn.T.DIST.2T(ABS(B22),B19)","v":6.4680699882726844E-2}]
[{"$f":"IF(B27<B5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]
[]
["Lower-Tail Test "]
["Lower Critical Value",{"$f":"-(_xlfn.T.INV.2T(2*B5,B19))","v":-1.7396067260750732}]
["p-Value",{"$f":"IF(B22<0,E21,E22)","v":3.2340349941363422E-2}]
[{"$f":"IF(B32<B5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Reject the null hypothesis"}]
[]
["Upper-Tail Test"]
["Upper Critical Value",{"$f":"(_xlfn.T.INV.2T(2*B5,B19))","v":1.7396067260750732}]
["p-Value",{"$f":"IF(B22<0,E22,E21)","v":0.96765965005863652}]
[{"$f":"IF(B37<B5,\"Reject the null hypothesis\",\"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]

{"sheet":"nuTSTTWS","index":54,"n_rows":38,"n_cols":5,"rows_kept":38,"cut":false,"hidden":false,"merged":[[14,0,14,1],[2,0,2,1],[2,3,2,4],[3,3,3,4],[5,3,5,4],[8,3,8,4],[13,3,13,4]]}
["Pooled-Variance t Test for the Difference Between Two Means"]
["(assumes equal population variances)"]
["Data",null,null,"Confidence Interval Estimate "]
["Hypothesized Difference",0,null,"for the Difference Between Two Means"]
["Level of Significance",0.05]
["Population 1 Sample",null,null,"Data"]
["Sample Size",10,null,"Confidence Level",0.95]
["Sample Mean",1]
["Sample Standard Deviation",1,null,"Intermediate Calculations"]
["Population 2 Sample",null,null,"Degrees of Freedom",{"$f":"B16+B17","v":18}]
["Sample Size",10,null,"t Value",{"$f":"_xlfn.T.INV.2T(1-E7, E10)","v":2.1009220402410378}]
["Sample Mean",2,null,"Interval Half Width",{"$f":"(E11*SQRT(B19*(1/B7+1/B11)))","v":1.4855762213987147}]
["Sample Standard Deviation",2]
[null,null,null,"Confidence Interval"]
["Intermediate Calculations",null,null,"Interval Lower Limit",{"$f":"B21-E12","v":-2.4855762213987145}]
["Population 1 Sample Degrees of Freedom",{"$f":"B7-1","v":9},null,"Interval Upper Limit",{"$f":"B21+E12","v":0.4855762213987147}]
["Population 2 Sample Degrees of Freedom",{"$f":"B11-1","v":9}]
["Total Degrees of Freedom",{"$f":"B16+B17","v":18}]
["Pooled Variance",{"$f":"((B16*B9^2)+(B17*B13^2))/B18","v":2.5}]
["Standard Error",{"$f":"SQRT(B19*(1/B7+1/B11))","v":0.70710678118654757}]
["Difference in Sample Means",{"$f":"B8-B12","v":-1}]
["t Test Statistic",{"$f":"(B21-B4)/B20","v":-1.4142135623730949}]
[]
["Two-Tail Test"]
["Lower Critical Value",{"$f":"-(_xlfn.T.INV.2T(B5, B18))","v":-2.1009220402410378}]
["Upper Critical Value",{"$f":"_xlfn.T.INV.2T(B5, B18)","v":2.1009220402410378}]
["p-Value",{"$f":"_xlfn.T.DIST.2T(ABS(B22), B18)","v":0.1743634883988705}]
[{"$f":"IF(B27<$B$5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]
[]
["Lower-Tail Test ",null,null,"Calculations Area"]
["Lower Critical Value",{"$f":"-(_xlfn.T.INV.2T(2*B5, B18))","v":-1.7340636066175394},null,"For one-tailed tests:"]
["p-Value",{"$f":"IF(B22<0, E32, E33)","v":8.7181744199435252E-2},null,"T.DIST.RT value",{"$f":"_xlfn.T.DIST.RT(ABS(B22), B18)","v":8.7181744199435252E-2}]
[{"$f":"IF(B32<$B$5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"},null,null,"1-T.DIST.RT value",{"$f":"1-E32","v":0.91281825580056475}]
[]
["Upper-Tail Test"]
["Upper Critical Value",{"$f":"(_xlfn.T.INV.2T(2*B5, B18))","v":1.7340636066175394}]
["p-Value",{"$f":"IF(B22<0, E33, E32)","v":0.91281825580056475}]
[{"$f":"IF(B37<$B$5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]

{"sheet":"nuTSZTWS","index":55,"n_rows":34,"n_cols":2,"rows_kept":34,"cut":false,"hidden":false,"merged":[[25,0,25,1],[28,0,28,1],[30,0,30,1],[33,0,33,1],[2,0,2,1],[5,0,5,1],[9,0,9,1],[14,0,14,1],[19,0,19,1],[23,0,23,1]]}
["Z Test for Differences in Two Means"]
[]
["Data"]
["Hypothesized Difference",0]
["Level of Significance",0.05]
["Population 1 Sample"]
["Sample Size",25]
["Sample Mean",5]
["Population Standard Deviation",3]
["Population 2 Sample"]
["Sample Size",45]
["Sample Mean",8]
["Population Standard Deviation",4]
[]
["Intermediate Calculations"]
["Difference in Sample Means",{"$f":"B8-B12","v":-3}]
["Standard Error of the Difference in Means",{"$f":"SQRT(((B9 ^ 2) / B7) + (B13 ^ 2) / B11)","v":0.84590516936330129}]
["Z Test Statistic",{"$f":"(B16-B4)/B17","v":-3.546496828075953}]
[]
["Two-Tail Test"]
["Lower Critical Value",{"$f":"_xlfn.NORM.S.INV(B5/2)","v":-1.9599639845400538}]
["Upper Critical Value",{"$f":"_xlfn.NORM.S.INV(1-(B5/2))","v":1.9599639845400536}]
["p-Value",{"$f":"2*(1-_xlfn.NORM.S.DIST(ABS(B18),TRUE))","v":3.9038944200298076E-4}]
[{"$f":"IF(B23<$B$5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Reject the null hypothesis"}]
[]
["Lower-Tail Test"]
["Lower Critical Value",{"$f":"_xlfn.NORM.S.INV(B5)","v":-1.6448536269514726}]
["p-Value",{"$f":"_xlfn.NORM.S.DIST(B18, TRUE)","v":1.9519472100144403E-4}]
[{"$f":"IF(B28 <$B$5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Reject the null hypothesis"}]
[]
["Upper-Tail Test"]
["Upper Critical Value",{"$f":"_xlfn.NORM.S.INV(1-B5)","v":1.6448536269514715}]
["p-Value",{"$f":"1-_xlfn.NORM.S.DIST(B18, TRUE)","v":0.99980480527899851}]
[{"$f":"IF(B33<$B$5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]

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["Z Test for Differences in Two Proportions"]
[]
["Data",null,null,"Confidence Interval Estimate "]
["Hypothesized Difference",0,null,"of the Difference Between Two Proportions"]
["Level of Significance",0.05]
["Group 1",null,null,"Data"]
["Number of Items of Interest",1,null,"Confidence Level",0.95]
["Sample Size",10]
["Group 2",null,null,"Intermediate Calculations"]
["Number of Items of Interest",2,null,"Z Value",{"$f":"_xlfn.NORM.S.INV((1-E7)/2)","v":-1.9599639845400536}]
["Sample Size",20,null,"Std. Error of the Diff. between two Proportions",{"$f":"SQRT((B14*(1-B14)/B8)+(B15*(1-B15)/B11))","v":0.11618950038622251}]
[null,null,null,"Interval Half Width",{"$f":"ABS(E10*E11)","v":0.22772723613869877}]
["Intermediate Calculations"]
["Group 1 Proportion",{"$f":"B7/B8","v":0.1},null,"Confidence Interval"]
["Group 2 Proportion",{"$f":"B10/B11","v":0.1},null,"Interval Lower Limit",{"$f":"B16-E12","v":-0.22772723613869877}]
["Difference in Two Proportions",{"$f":"B14-B15","v":0},null,"Interval Upper Limit",{"$f":"B16+E12","v":0.22772723613869877}]
["Average Proportion",{"$f":"(B7+B10)/(B8+B11)","v":0.1}]
["Z Test Statistic",{"$f":"(B16-B4)/SQRT(B17*(1-B17)*(1/B8+1/B11))","v":0}]
[]
["Two-Tail Test"]
["Lower Critical Value",{"$f":"_xlfn.NORM.S.INV(B5/2)","v":-1.9599639845400538}]
["Upper Critical Value",{"$f":"_xlfn.NORM.S.INV(1-B5/2)","v":1.9599639845400536}]
["p-Value",{"$f":"2*(1-_xlfn.NORM.S.DIST(ABS(B18),TRUE))","v":1}]
[{"$f":"IF(B23<$B$5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]
[]
["Lower-Tail Test"]
["Lower Critical Value",{"$f":"_xlfn.NORM.S.INV(B5)","v":-1.6448536269514726}]
["p-Value",{"$f":"_xlfn.NORM.S.DIST(B18,TRUE)","v":0.5}]
[{"$f":"IF(B28<$B$5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]
[]
["Upper-Tail Test"]
["Upper Critical Value",{"$f":"_xlfn.NORM.S.INV(1-B5)","v":1.6448536269514715}]
["p-Value",{"$f":"1-_xlfn.NORM.S.DIST(B18,TRUE )","v":0.5}]
[{"$f":"IF(B33<$B$5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]

{"sheet":"nuTSFTWS","index":57,"n_rows":28,"n_cols":5,"rows_kept":28,"cut":false,"hidden":false,"merged":[[2,0,2,1],[11,0,11,1]]}
["F Test for Differences in Two Variances"]
[]
["Data"]
["Level of Significance",0.05]
["Larger-Variance Sample"]
["Sample Size",10]
["Sample Variance",1]
["Smaller-Variance Sample"]
["Sample Size",10]
["Sample Variance",1]
[]
["Intermediate Calculations"]
["F Test Statistic",{"$f":"B7/B10","v":1}]
["Population 1 Sample Degrees of Freedom",{"$f":"B6-1","v":9}]
["Population 2 Sample Degrees of Freedom",{"$f":"B9-1","v":9}]
[null,null,null,"Calculations Area"]
["Two-Tail Test",null,null,"F.DIST.RT value",{"$f":"_xlfn.F.DIST.RT(B13, B14, B15)","v":0.49999999999999989}]
["Upper Critical Value",{"$f":"_xlfn.F.INV.RT(B4/2, B14, B15)","v":4.0259941582829777}]
["p-Value",{"$f":"2*E17","v":0.99999999999999978}]
[{"$f":"IF(B19<B4, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]
[]
["Upper-Tail Test"]
["Upper Critical Value",{"$f":"_xlfn.F.INV.RT(B4, B14, B15)","v":3.17889310445827}]
["p-Value",{"$f":"E17","v":0.49999999999999989}]
[{"$f":"IF(B24<B4, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]
[]
[{"$f":"IF(B7<B10, \"Error: Review your entries for cells B6:B7 and B9:B10.\", \"\")","v":""}]
[{"$f":"IF(B7<B10, \"You entered the largest standard deviation as part of the Smaller-Variance Sample.\", \"\")","v":""}]

{"sheet":"nuWilcoxonWS","index":58,"n_rows":34,"n_cols":2,"rows_kept":34,"cut":false,"hidden":false,"merged":[[12,0,12,1]]}
["Wilcoxon Rank Sum Test for Differences in Two Medians"]
[]
["Data"]
["Level of Significance",0.05]
[]
["Population 1 Sample"]
["Sample Size",1]
["Sum of Ranks",1]
["Population 2 Sample"]
["Sample Size",1]
["Sum of Ranks",1]
[]
["Intermediate Calculations"]
["Total Sample Size n",{"$f":"B7+B10","v":2}]
["T1 Test Statistic",{"$f":"IF(B7<=B10,B8,B11)","v":1}]
["T1 Mean",{"$f":"IF(B7<=B10,B7*(B14+1)/2,B10*(B14+1)/2)","v":1.5}]
["Standard Error of T1",{"$f":"SQRT(B7*B10*(B14+1)/12)","v":0.5}]
["Z Test Statistic",{"$f":"(B15-B16)/B17","v":-1}]
[]
["Two-Tail Test"]
["Lower Critical Value",{"$f":"_xlfn.NORM.S.INV(B4/2)","v":-1.9599639845400538}]
["Upper Critical Value",{"$f":"_xlfn.NORM.S.INV(1-B4/2)","v":1.9599639845400536}]
["p-Value",{"$f":"2*(1-_xlfn.NORM.S.DIST(ABS(B18), TRUE))","v":0.31731050786291393}]
[{"$f":"IF(B23<$B$4, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]
[]
["Lower-Tail Test"]
["Lower Critical Value",{"$f":"_xlfn.NORM.S.INV(B4)","v":-1.6448536269514726}]
["p-Value",{"$f":"_xlfn.NORM.S.DIST(B18, TRUE)","v":0.15865525393145699}]
[{"$f":"IF(B28<$B$4, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]
[]
["Upper-Tail Test"]
["Upper Critical Value",{"$f":"_xlfn.NORM.S.INV(1-B4)","v":1.6448536269514715}]
["p-Value",{"$f":"1-_xlfn.NORM.S.DIST(B18, TRUE)","v":0.84134474606854304}]
[{"$f":"IF(B33<$B$4, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]

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["Z Test of Hypothesis for the Proportion"]
[]
["Data"]
["Null Hypothesis            p =",0.1]
["Level of Significance",0.05]
["Number of Items of Interest",11]
["Sample Size",200]
[]
["Intermediate Calculations"]
["Sample Proportion",{"$f":"B6/B7","v":5.5E-2}]
["Standard Error",{"$f":"SQRT(B4*(1-B4)/B7)","v":2.1213203435596427E-2}]
["Z Test Statistic",{"$f":"(B10-B4)/B11","v":-2.1213203435596428}]
[]
["Two-Tail Test"]
["Lower Critical Value",{"$f":"_xlfn.NORM.S.INV(B5/2)","v":-1.9599639845400538}]
["Upper Critical Value",{"$f":"_xlfn.NORM.S.INV(1-B5/2)","v":1.9599639845400536}]
["p-Value",{"$f":"2*(1-_xlfn.NORM.S.DIST(ABS(B12), TRUE))","v":3.3894853524689239E-2}]
[{"$f":"IF(B17<$B$5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Reject the null hypothesis"}]
[]
["Lower-Tail Test"]
["Lower Critical Value",{"$f":"_xlfn.NORM.S.INV(B5)","v":-1.6448536269514726}]
["p-Value",{"$f":"_xlfn.NORM.S.DIST(B12, TRUE)","v":1.6947426762344623E-2}]
[{"$f":"IF(B22<$B$5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Reject the null hypothesis"}]
[]
["Upper-Tail Test"]
["Upper Critical Value",{"$f":"_xlfn.NORM.S.INV(1-B5)","v":1.6448536269514715}]
["p-Value",{"$f":"1-_xlfn.NORM.S.DIST(B12, TRUE)","v":0.98305257323765538}]
[{"$f":"IF(B27<$B$5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]

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["t Test for the Hypothesis of the Mean"]
[]
["Data"]
["Null Hypothesis                m=",120]
["Level of Significance",0.05]
["Sample Size",2]
["Sample Mean",1]
["Sample Standard Deviation",1]
[]
["Intermediate Calculations"]
["Standard Error of the Mean",{"$f":"B8/SQRT(B6)","v":0.70710678118654746}]
["Degrees of Freedom",{"$f":"B6-1","v":1}]
["t Test Statistic",{"$f":"(B7-B4)/B11","v":-168.29141392239833}]
[]
["Two-Tail Test"]
["Lower Critical Value",{"$f":"-(_xlfn.T.INV.2T(B5, B12))","v":-12.706204736174707}]
["Upper Critical Value",{"$f":"_xlfn.T.INV.2T(B5, B12)","v":12.706204736174707}]
["p-Value",{"$f":"_xlfn.T.DIST.2T(ABS(B13), B12)","v":3.7827971436405097E-3}]
[{"$f":"IF(B18<$B$5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Reject the null hypothesis"}]
[null,null,null,"Calculations Area"]
["Lower-Tail Test",null,null,"For one-tailed tests:"]
["Lower Critical Value",{"$f":"-(_xlfn.T.INV.2T(2*B5, B12))","v":-6.3137515146750438},null,"T.DIST.RT value",{"$f":"_xlfn.T.DIST.RT(ABS(B13), B12)","v":1.8913985718202549E-3}]
["p-Value",{"$f":"IF(B13<0, E22, E23)","v":1.8913985718202549E-3},null,"1-T.DIST.RT value",{"$f":"1-E22","v":0.9981086014281797}]
[{"$f":"IF(B23<$B$5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Reject the null hypothesis"}]
[]
["Upper-Tail Test"]
["Upper Critical Value",{"$f":"(_xlfn.T.INV.2T(2*B5, B12))","v":6.3137515146750438}]
["p-Value",{"$f":"IF(B13<0, E23, E22)","v":0.9981086014281797}]
[{"$f":"IF(B28<$B$5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]

{"sheet":"nuZTMeanWS","index":61,"n_rows":28,"n_cols":2,"rows_kept":28,"cut":false,"hidden":false,"merged":[[2,0,2,1],[9,0,9,1]]}
["Z Test of the Hypothesis for the Mean"]
[]
["Data"]
["Null Hypothesis                       m=",1]
["Level of Significance",0.05]
["Population Standard Deviation",2]
["Sample Size",10]
["Sample Mean",1]
[]
["Intermediate Calculations"]
["Standard Error of the Mean",{"$f":"B6/SQRT(B7)","v":0.63245553203367588}]
["Z Test Statistic",{"$f":"(B8-B4)/B11","v":0}]
[]
["Two-Tail Test"]
["Lower Critical Value",{"$f":"_xlfn.NORM.S.INV(B5/2)","v":-1.9599639845400538}]
["Upper Critical Value",{"$f":"_xlfn.NORM.S.INV(1-B5/2)","v":1.9599639845400536}]
["p-Value",{"$f":"2*(1-_xlfn.NORM.S.DIST(ABS(B12), TRUE))","v":1}]
[{"$f":"IF(B17<$B$5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]
[]
["Lower-Tail Test"]
["Lower Critical Value",{"$f":"_xlfn.NORM.S.INV(B5)","v":-1.6448536269514726}]
["p-Value",{"$f":"_xlfn.NORM.S.DIST(B12, TRUE)","v":0.5}]
[{"$f":"IF(B22<$B$5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]
[]
["Upper-Tail Test"]
["Upper Critical Value",{"$f":"_xlfn.NORM.S.INV(1-B5)","v":1.6448536269514715}]
["p-Value",{"$f":"1-_xlfn.NORM.S.DIST(B12, TRUE)","v":0.5}]
[{"$f":"IF(B27<$B$5, \"Reject the null hypothesis\", \"Do not reject the null hypothesis\")","v":"Do not reject the null hypothesis"}]

{"sheet":"nuCITDWS","index":62,"n_rows":21,"n_cols":5,"rows_kept":21,"cut":false,"hidden":false,"merged":[[2,0,2,1],[7,0,7,1],[18,0,18,1]]}
["Confidence Interval Estimate for the Total Difference"]
[]
["Data"]
["Population Size",5000]
["Sample Size",100]
["Confidence Level",0.95]
[]
["Intermediate Calculations"]
["Sum of Differences","=SUM(Data!A:A)",null,"Calculations Area"]
["Average Difference in Sample",{"$f":"B9/B5","v":{"$error":"#VALUE!"}},null,"For standard deviation of differences:"]
["Total Difference",{"$f":"B4*B10","v":{"$error":"#VALUE!"}},null,"Number of Differences Not = 0","=COUNT(Data!A:A)"]
["Standard Deviation of Differences",{"$f":"SQRT(E16)","v":{"$error":"#VALUE!"}},null,"Number of Differences = 0",{"$f":"B5-E11","v":{"$error":"#VALUE!"}}]
["FPC Factor",{"$f":"SQRT((B4-B5)/(B4-1))","v":0.99004850346225037},null,"SS for Differences Not = 0","=SUM(Data!B:B)"]
["Standard Error of the Total Diff.",{"$f":"(B4*B12*B13)/SQRT(B5)","v":{"$error":"#VALUE!"}},null,"SS for Differences = 0",{"$f":"E12*(-B10)^2","v":{"$error":"#VALUE!"}}]
["Degrees of Freedom",{"$f":"B5-1","v":99},null,"Sum of Squares",{"$f":"E13+E14","v":{"$error":"#VALUE!"}}]
["t Value",{"$f":"_xlfn.T.INV.2T(1-B6,B15)","v":1.9842169515864165},null,"Variance of Differences",{"$f":"E15/B15","v":{"$error":"#VALUE!"}}]
["Interval Half Width",{"$f":"B16*B14","v":{"$error":"#VALUE!"}}]
[]
["Confidence Interval"]
["Interval Lower Limit",{"$f":"B11-B17","v":{"$error":"#VALUE!"}}]
["Interval Upper Limit",{"$f":"B11+B17","v":{"$error":"#VALUE!"}}]

{"sheet":"nuCIPTWS","index":63,"n_rows":20,"n_cols":2,"rows_kept":20,"cut":false,"hidden":false,"merged":[[9,0,9,1],[17,0,17,1]]}
["Confidence Interval Estimate for the Population Total"]
[]
["Data"]
["Population Size",5000]
["Sample Mean",100]
["Sample Size",100]
["Sample Standard Deviation",20]
["Confidence Level",0.95]
[]
["Intermediate Calculations"]
["Population Total",{"$f":"B4*B5","v":500000}]
["FPC Factor",{"$f":"SQRT((B4-B6)/(B4-1))","v":0.99004850346225037}]
["Standard Error of the Total",{"$f":"(B4*B7*B12)/SQRT(B6)","v":9900.485034622503}]
["Degrees of Freedom",{"$f":"B6-1","v":99}]
["t Value",{"$f":"_xlfn.T.INV.2T(1-B8,B14)","v":1.9842169515864165}]
["Interval Half Width",{"$f":"B15*B13","v":19644.7102346256}]
[]
["Confidence Interval"]
["Interval Lower Limit",{"$f":"B11-B16","v":480355.28976537439}]
["Interval Upper Limit",{"$f":"B11+B16","v":519644.71023462561}]

{"sheet":"nuSSPWS","index":64,"n_rows":19,"n_cols":2,"rows_kept":19,"cut":false,"hidden":false,"merged":[[7,0,7,1],[11,0,11,1]]}
["Sample Size for Estimating the Proportion"]
[]
["Data"]
["Estimate of True Proportion",0.15]
["Sampling Error",7.0000000000000007E-2]
["Confidence Level",0.95]
[]
["Intermediate Calculations"]
["Z Value",{"$f":"_xlfn.NORM.S.INV((1-B6)/2)","v":-1.9599639845400536}]
["Calculated Sample Size ",{"$f":"(B9^2*B4*(1-B4))/B5^2","v":99.956326456836862}]
[]
["Result"]
["Sample Size Needed",{"$f":"ROUNDUP(B10, 0)","v":100}]
[]
[]
["Finite Populations"]
["Population Size",5000]
["Calculated Sample Size",{"$f":"(B10*B17)/(B10+B17-1)","v":98.016456758215185}]
["Sample Size Needed",{"$f":"ROUNDUP(B18, 0)","v":99}]

{"sheet":"nuSSMWS","index":65,"n_rows":19,"n_cols":2,"rows_kept":19,"cut":false,"hidden":false,"merged":[[7,0,7,1],[11,0,11,1]]}
["Sample Size for Estimating the Mean"]
[]
["Data"]
["Population Standard Deviation",25]
["Sampling Error",5]
["Confidence Level",0.95]
[]
["Intemediate Calculations"]
["Z Value",{"$f":"_xlfn.NORM.S.INV((1-B6)/2)","v":-1.9599639845400536}]
["Calculated Sample Size ",{"$f":"((B9*B4)/B5)^2","v":96.036470517353109}]
[]
["Result"]
["Sample Size Needed",{"$f":"ROUNDUP(B10, 0)","v":97}]
[]
[]
["Finite Populations"]
["Population Size",5000]
["Sample Size with FPC",{"$f":"(B10*B17)/(B10+B17-1)","v":94.245125695441288}]
["Sample Size Needed",{"$f":"ROUNDUP(B18, 0)","v":95}]

{"sheet":"nuCIPWS","index":66,"n_rows":24,"n_cols":2,"rows_kept":24,"cut":false,"hidden":false,"merged":[[7,0,7,1],[13,0,13,1]]}
["Confidence Interval Estimation for the Proportion"]
[]
["Data"]
["Sample Size",100]
["Number of Successes",10]
["Confidence Level",0.95]
[]
["Intermediate Calculations"]
["Sample Proportion",{"$f":"B5/B4","v":0.1}]
["Z Value",{"$f":"_xlfn.NORM.S.INV((1-B6)/2)","v":-1.9599639845400536}]
["Standard Error of the Proportion",{"$f":"SQRT(B9*(1-B9)/B4)","v":3.0000000000000002E-2}]
["Interval Half Width",{"$f":"ABS(B10*B11)","v":5.8798919536201616E-2}]
[]
["Confidence Interval"]
["Interval Lower Limit",{"$f":"B9-B12","v":4.120108046379839E-2}]
["Interval Upper Limit",{"$f":"B9+B12","v":0.15879891953620162}]
[]
[]
["Finite Populations"]
["Population Size",5000]
["FPC Factor",{"$f":"SQRT((B20-B4)/(B20-1))","v":0.99004850346225037}]
["Interval Half Width",{"$f":"B12*B21","v":5.821378229201369E-2}]
["Interval Lower Limit",{"$f":"B9-B22","v":4.1786217707986316E-2}]
["Interval Upper Limit",{"$f":"B9+B22","v":0.15821378229201369}]

{"sheet":"nuCIMSUWS","index":67,"n_rows":25,"n_cols":2,"rows_kept":25,"cut":false,"hidden":false,"merged":[[8,0,8,1],[14,0,14,1]]}
["Confidence Interval Estimate for the Mean"]
[]
["Data"]
["Sample Standard Deviation",20]
["Sample Mean",10]
["Sample Size",100]
["Confidence Level",0.95]
[]
["Intermediate Calculations"]
["Standard Error of the Mean",{"$f":"B4/SQRT(B6)","v":2}]
["Degrees of Freedom",{"$f":"B6-1","v":99}]
["t Value",{"$f":"_xlfn.T.INV.2T(1-B7, B11)","v":1.9842169515864165}]
["Interval Half Width",{"$f":"B12*B10","v":3.9684339031728331}]
[]
["Confidence Interval"]
["Interval Lower Limit",{"$f":"B5-B13","v":6.0315660968271665}]
["Interval Upper Limit",{"$f":"B5+B13","v":13.968433903172834}]
[]
[]
["Finite Populations"]
["Population Size",5000]
["FPC Factor",{"$f":"SQRT((B21-B6)/(B21-1))","v":0.99004850346225037}]
["Interval Half Width",{"$f":"B13*B22","v":3.9289420469251204}]
["Interval Lower Limit",{"$f":"B5-B23","v":6.0710579530748792}]
["Interval Upper Limit",{"$f":"B5+B23","v":13.928942046925121}]

{"sheet":"nuCIMSKWS","index":68,"n_rows":24,"n_cols":2,"rows_kept":24,"cut":false,"hidden":false,"merged":[[8,0,8,1],[13,0,13,1]]}
["Confidence Interval Estimate for the Mean"]
[]
["Data"]
["Population Standard Deviation",0.02]
["Sample Mean",10]
["Sample Size",100]
["Confidence Level",0.95]
[]
["Intermediate Calculations"]
["Standard Error of the Mean",{"$f":"B4/SQRT(B6)","v":2E-3}]
["Z Value",{"$f":"_xlfn.NORM.S.INV((1-B7)/2)","v":-1.9599639845400536}]
["Interval Half Width",{"$f":"_xlfn.CONFIDENCE.NORM(1-B7, B4, B6)","v":3.9199279690801071E-3}]
[]
["Confidence Interval"]
["Interval Lower Limit",{"$f":"B5-B12","v":9.9960800720309191}]
["Interval Upper Limit",{"$f":"B5+B12","v":10.003919927969081}]
[]
[]
["Finite Populations"]
["Population Size",10000]
["FPC Factor",{"$f":"SQRT((B20-B6)/(B20-1))","v":0.99503719020998915}]
["Interval Half Width",{"$f":"B12*B21","v":3.9004741121790188E-3}]
["Interval Lower Limit",{"$f":"B5-B22","v":9.9960995258878214}]
["Interval Upper Limit",{"$f":"B5+B22","v":10.003900474112179}]

{"sheet":"nuExponentialWS","index":69,"n_rows":8,"n_cols":2,"rows_kept":8,"cut":false,"hidden":false,"merged":[[2,0,2,1],[6,0,6,1]]}
["Exponential Probability"]
[]
["Data"]
["Mean",20]
["X Value",0.1]
[]
["Results"]
["P(<=X)",{"$f":"_xlfn.EXPON.DIST(B5, B4, TRUE)","v":0.8646647167633873}]

{"sheet":"nuNormalWS","index":70,"n_rows":38,"n_cols":2,"rows_kept":38,"cut":false,"hidden":false,"merged":[[33,0,33,1],[16,0,16,1],[2,0,2,1],[19,0,19,1],[6,0,6,1],[11,0,11,1],[28,0,28,1]]}
["Normal Probabilities"]
[]
["Common Data"]
["Mean",7]
["Standard Deviation",2]
[]
["Probability for X <="]
["X Value",7]
["Z Value",{"$f":"STANDARDIZE(B8, B4, B5)","v":0}]
[{"$f":"\"P(X<=\"&B8&\")\"","v":"P(X<=7)"},{"$f":"_xlfn.NORM.DIST(B8, B4, B5, TRUE)","v":0.5}]
[]
["Probability for X >"]
["X Value",9]
["Z Value",{"$f":"STANDARDIZE(B13, B4, B5)","v":1}]
[{"$f":"\"P(X>\"&B13&\")\"","v":"P(X>9)"},{"$f":"1-_xlfn.NORM.DIST(B13, B4, B5, TRUE)","v":0.15865525393145696}]
[]
[{"$f":"\"Probability for X<\"&B8&\" or X >\"&B13","v":"Probability for X<7 or X >9"}]
[{"$f":"\"P(X<\"&B8&\" or X >\"&B13 & \")\"","v":"P(X<7 or X >9)"},{"$f":"B10+B15","v":0.65865525393145696}]
[]
["Probability for a Range"]
["From X Value",5]
["To X Value",9]
[{"$f":"\"Z Value for \" &B21","v":"Z Value for 5"},{"$f":"STANDARDIZE(B21, B4, B5)","v":-1}]
[{"$f":"\"Z Value for \" & B22","v":"Z Value for 9"},{"$f":"STANDARDIZE(B22, B4, B5)","v":1}]
[{"$f":"\"P(X<=\"&B21&\")\"","v":"P(X<=5)"},{"$f":"_xlfn.NORM.DIST(B21, B4, B5, TRUE)","v":0.15865525393145699}]
[{"$f":"\"P(X<=\"&B22&\")\"","v":"P(X<=9)"},{"$f":"_xlfn.NORM.DIST(B22, B4, B5, TRUE)","v":0.84134474606854304}]
[{"$f":"\"P(\"&B21&\"<=X<=\"&B22&\")\"","v":"P(5<=X<=9)"},{"$f":"ABS(B26-B25)","v":0.68268949213708607}]
[]
["Find X and Z Given Cum. Pctage."]
["Cumulative Percentage",0.1]
["Z Value",{"$f":"_xlfn.NORM.S.INV(B30)","v":-1.2815515655446006}]
["X Value",{"$f":"_xlfn.NORM.INV(B30, B4, B5)","v":4.4368968689107984}]
[]
["Find X Values Given a Percentage"]
["Percentage",0.95]
["Z Value",{"$f":"_xlfn.NORM.S.INV((1 - B35)/2)","v":-1.9599639845400536}]
["Lower X Value",{"$f":"B4 + B36 * B5","v":3.0800720309198928}]
["Upper X Value",{"$f":"B4 - B36 * B5","v":10.919927969080106}]

{"sheet":"nuHypergeoWS","index":71,"n_rows":11,"n_cols":3,"rows_kept":11,"cut":false,"hidden":false,"merged":[[2,0,2,1]]}
["Hypergeometric Probabilities"]
[]
["Data"]
["Sample size",1]
["No. of events of interest in population",1]
["Population size",2]
[]
["Hypergeometric Probabilities Table"]
[null,"X","P(X)"]
[null,0,{"$f":"_xlfn.HYPGEOM.DIST(B10, $B$4, $B$5, $B$6, FALSE)","v":0.5}]
[null,1,{"$f":"_xlfn.HYPGEOM.DIST(B11, $B$4, $B$5, $B$6, FALSE)","v":0.5}]

{"sheet":"nuPoissonWS","index":72,"n_rows":28,"n_cols":7,"rows_kept":28,"cut":false,"hidden":false,"merged":[[2,0,2,4]]}
["POISSON.DIST Probabilities"]
[]
["Data"]
["Mean/Expected number of events of interest:",null,null,null,3]
[]
["POISSON.DIST Probabilities Table"]
[null,"X","P(X)","P(<=X)","P(<X)","P(>X)","P(>=X)"]
[null,0,{"$f":"_xlfn.POISSON.DIST(B8, $E$4, FALSE)","v":4.9787068367863944E-2},{"$f":"_xlfn.POISSON.DIST(B8, $E$4, TRUE)","v":4.9787068367863944E-2},{"$f":"D8-C8","v":0},{"$f":"1-D8","v":0.95021293163213605},{"$f":"1-E8","v":1}]
[null,1,0.14936120510359185,0.19914827347145578,{"$f":"D9-C9","v":4.9787068367863924E-2},{"$f":"1-D9","v":0.80085172652854419},0.95021293163213605]
[null,2,0.22404180765538775,0.42319008112684342,0.19914827347145567,0.57680991887315658,0.80085172652854431]
[null,3,0.22404180765538778,0.64723188878223126,0.42319008112684348,0.35276811121776874,0.57680991887315658]
[null,4,0.16803135574154085,0.81526324452377208,0.64723188878223126,0.18473675547622792,0.35276811121776874]
[null,5,0.10081881344492449,0.91608205796869657,0.81526324452377208,8.3917942031303427E-2,0.18473675547622792]
[null,6,5.0409406722462261E-2,0.96649146469115887,0.91608205796869657,3.3508535308841125E-2,8.3917942031303427E-2]
[null,7,2.1604031452483807E-2,0.98809549614364256,0.96649146469115876,1.190450385635744E-2,3.3508535308841236E-2]
[null,8,8.1015117946814375E-3,0.996197007938324,0.98809549614364256,3.8029920616760027E-3,1.190450385635744E-2]
[null,9,2.7005039315604771E-3,0.99889751186988451,0.996197007938324,1.1024881301154865E-3,3.8029920616760027E-3]
[null,10,8.1015117946814244E-4,0.99970766304935266,0.99889751186988451,2.9233695064734277E-4,1.1024881301154865E-3]
[null,11,2.2095032167312987E-4,0.99992861337102579,0.99970766304935266,7.1386628974212663E-5,2.9233695064734277E-4]
[null,12,5.5237580418282596E-5,0.99998385095144404,0.99992861337102579,1.614904855595789E-5,7.1386628974212663E-5]
[null,13,1.2747133942680586E-5,0.99999659808538677,0.99998385095144404,3.4019146132324707E-6,1.614904855595789E-5]
[null,14,2.7315287020029766E-6,0.99999932961408877,0.99999659808538677,6.7038591122781099E-7,3.4019146132324707E-6]
[null,15,5.4630574040059675E-7,0.9999998759198292,0.99999932961408877,1.2408017080467459E-7,6.7038591122781099E-7]
[null,16,1.0243232632511179E-7,0.99999997835215548,{"$f":"D24-C24","v":0.9999998759198292},2.1647844516969883E-8,{"$f":"1-E24","v":1.2408017080467459E-7}]
[null,17,1.8076292880902042E-8,0.99999999642844839,{"$f":"D25-C25","v":0.99999997835215548},{"$f":"1-D25","v":3.5715516100154332E-9},{"$f":"1-E25","v":2.1647844516969883E-8}]
[null,18,3.0127154801503488E-9,0.99999999944116391,{"$f":"D26-C26","v":0.99999999642844839},5.5883608851559075E-10,{"$f":"1-E26","v":3.5715516100154332E-9}]
[null,19,4.7569191791847703E-10,0.99999999991685584,{"$f":"D27-C27","v":0.99999999944116391},8.3144158224968123E-11,{"$f":"1-E27","v":5.5883608851559075E-10}]
[null,20,7.1353787687771353E-11,0.99999999998820954,{"$f":"D28-C28","v":0.99999999991685573},1.17904574992167E-11,{"$f":"1-E28","v":8.3144269247270586E-11}]

{"sheet":"nuBinomialWS","index":73,"n_rows":14,"n_cols":7,"rows_kept":14,"cut":false,"hidden":false,"merged":[[2,0,2,1],[6,0,6,1]]}
["Binomial Probabilities"]
[]
["Data"]
["Sample size",4]
["Probability of an event of interest",1]
[]
["Statistics"]
["Mean",{"$f":"B4*B5","v":4}]
["Variance",{"$f":"B8*(1-B5)","v":0}]
["Standard deviation",{"$f":"SQRT(B9)","v":0}]
[]
["Binomial Probabilities Table"]
[null,"X","P(X)","P(<=X)","P(<X)","P(>X)","P(>=X)"]
[null,0,{"$f":"_xlfn.BINOM.DIST(B14, $B$4, $B$5, FALSE)","v":{"$error":"#NUM!"}},{"$f":"_xlfn.BINOM.DIST(B14, $B$4, $B$5, TRUE)","v":0},{"$f":"D14-C14","v":{"$error":"#NUM!"}},{"$f":"1-D14","v":1},{"$f":"1-E14","v":{"$error":"#NUM!"}}]

{"sheet":"Basic Probabilities","index":74,"n_rows":25,"n_cols":5,"rows_kept":25,"cut":false,"hidden":false,"merged":[[8,0,8,1],[14,0,14,1],[20,0,20,1]]}
["Probabilities Calculations"]
[]
["Sample Space",null,"Event B"]
[null,null,"B1","B2","Totals"]
["Event A","A1",1,1,{"$f":"C5+D5","v":2}]
[null,"A2",1,1,{"$f":"C6+D6","v":2}]
[null,"Totals",{"$f":"C5+C6","v":2},{"$f":"D5+D6","v":2},{"$f":"C7+D7","v":4}]
[]
["Simple Probabilities"]
[{"$f":"\"P(\"&B5&\")\"","v":"P(A1)"},{"$f":"E5/E7","v":0.5}]
[{"$f":"\"P(\"&B6&\")\"","v":"P(A2)"},{"$f":"E6/E7","v":0.5}]
[{"$f":"\"P(\"&C4&\")\"","v":"P(B1)"},{"$f":"C7/E7","v":0.5}]
[{"$f":"\"P(\"&D4&\")\"","v":"P(B2)"},{"$f":"D7/E7","v":0.5}]
[]
["Joint Probabilities"]
[{"$f":"\"P(\"&B5&\" and \"&C4&\")\"","v":"P(A1 and B1)"},{"$f":"C5/E7","v":0.25}]
[{"$f":"\"P(\"&B5&\" and \"&D4&\")\"","v":"P(A1 and B2)"},{"$f":"D5/E7","v":0.25}]
[{"$f":"\"P(\"&B6&\" and \"&C4&\")\"","v":"P(A2 and B1)"},{"$f":"C6/E7","v":0.25}]
[{"$f":"\"P(\"&B6&\" and \"&D4&\")\"","v":"P(A2 and B2)"},{"$f":"D6/E7","v":0.25}]
[]
["Addition Rule"]
[{"$f":"\"P(\"&B5&\" or \"&C4&\")\"","v":"P(A1 or B1)"},{"$f":"B10+B12-B16","v":0.75}]
[{"$f":"\"P(\"&B5&\" or \"&D4&\")\"","v":"P(A1 or B2)"},{"$f":"B10+B13-B17","v":0.75}]
[{"$f":"\"P(\"&B6&\" or \"&C4&\")\"","v":"P(A2 or B1)"},{"$f":"B11+B12-B18","v":0.75}]
[{"$f":"\"P(\"&B6&\" or \"&D4&\")\"","v":"P(A2 or B2)"},{"$f":"B11+B13-B19","v":0.75}]