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[null,null,"Sample Final Exam answers"]
[]
[null,"1a)",{"$f":"0.2+0.3-0.1","v":0.4},{"$f":"showformula(C3)","v":"=0.2+0.3-0.1"},null,"Pr(A or B) = Pr(A) + Pr(B) - Pr(A and B) "]
[null,"1b)","no","Pr(A and B) ≠ Pr(A)×Pr(B)"]
[null,"1c)",{"$f":"0.1/0.3","v":0.33333333333333337},{"$f":"showformula(C5)","v":"=0.1/0.3"},null,"Pr(A|B) = Pr(A and B) / Pr(B)"]
[]
[null,"2a)",{"$f":"1/3","v":0.33333333333333331},"common sense"]
[null,"2b)",{"$f":"5/14*9/13+9/14*5/13","v":0.49450549450549453},{"$f":"showformula(C8)","v":"=5/14*9/13+9/14*5/13"},null,null,"Given that the first has an MBA, there are 14 left, 5 with MBAs."]
[null,null,null,null,null,null,"Pick two of these: What’s the chance of getting one MBA and one non-MBA?  "]
[]
[null,"2c)",{"$f":"(6/15)/(1-(9/15)*(8/14)*(7/13))","v":0.49056603773584911},{"$f":"showformula(C11)","v":"=(6/15)/(1-(9/15)*(8/14)*(7/13))"},null,null,null,"Pr(1st has MBA | at least one MBA)"]
[null,null,null,null,null,null,null,"= Pr(1st has MBA and at least one MBA) / Pr(at least one MBA)"]
[null,null,null,null,null,null,null,"= Pr(1st has MBA) / (1 – Pr(no MBAs))"]
[]
[null,"3a)",{"$f":"NORMDIST(101,100+0.1,0.5,TRUE)-NORMDIST(99.5,100+0.1,0.5,TRUE)","v":0.84900001066536468},{"$f":"showformula(C15)","v":"=NORMDIST(101,100+0.1,0.5,TRUE)-NORMDIST(99.5,100+0.1,0.5,TRUE)"}]
[null,"3b)",{"$f":"NORMDIST(111,100+52*0.1,SQRT(52)*0.5,TRUE)-NORMDIST(99,100+52*0.1,SQRT(52)*0.5,TRUE)","v":0.90339616575793513},"=NORMDIST(111,100+52*0.1,SQRT(52)*0.5,TRUE)-NORMDIST(99,100+52*0.1,SQRT(52)*0.5,TRUE)"]
[]
[null,"4)",{"$f":"1-(1/2)^5","v":0.96875},"=1-(1/2)^5"]
[null,null,{"$f":"5*(1/2)","v":2.5},"=5*(1/2)"]
[null,null,null,""]
[null,"5)",{"$f":"(1-0.1)^3*0.1","v":7.2900000000000006E-2},"=(1-0.1)^3*0.1"]
[]
[null,"6a) ",14.5,"±",{"$f":"_xlfn.T.INV(0.975, 224)*8.2/SQRT(225)","v":1.0772673254026255},{"$f":"showformula(E23)","v":"=T.INV(0.975, 224)*8.2/SQRT(225)"}]
[null,"6b)",{"$f":"(14.5-15.5) /(8.2/SQRT(225))","v":-1.8292682926829269},{"$f":"showformula(C24)","v":"=(14.5-15.5) /(8.2/SQRT(225))"},null,null,"The test statistic is t = (14.5-m)/(s/Ön),"]
[null,null,{"$f":" _xlfn.T.DIST(C24,225-1,TRUE)","v":3.4344413497243945E-2},"= T.DIST(C24,225-1,TRUE)",null,null,"and so the significance level is = 3.4344%. Or:"]
[]
[null,null,14.5,"estimate/prediction of unknown quantity"]
[null,null,{"$f":"8.2/SQRT(225)","v":0.54666666666666663},"measure of uncertainty"]
[null,null,225,"sample size"]
[null,null,0,"number of explanatory variables in regression, or"]
[null,null,null,"0 if dealing with a population mean"]
[]
[null,null,null,null,null,null,null,null,"significance level of data with respect to null hypothesis"]
[null,null,"Null hypothesis:"]
[null,null,null,null,null,"≥",null,null,null,{"$f":"IF(C27>=G36,1,TDIST((G36-C27)/C28,C29-1-C30,TRUE))","v":3.4344413497243945E-2}]
[null,null,null,null,"true value   ","=",15.5,null,null,{"$f":"2*TDIST(ABS(G36-C27)/C28,C29-1-C30,TRUE)","v":6.8688826994487889E-2}]
[null,null,null,null,null,"≤",null,null,null,{"$f":"IF(G36>=C27,1,TDIST((C27-G36)/C28,C29-1-C30,TRUE))","v":1}]
[null,null,null,null,null,null,null,null,null,{"$f":"\"(from t-distribution with \"&TEXT(C29-1-C30,\"0\")&\" degrees of freedom)\"","v":"(from t-distribution with 224 degrees of freedom)"}]
[]
[null,"7a)",{"$f":"42/300","v":0.14000000000000001},{"$f":"showformula(C40)","v":"=42/300"}]
[null,"7b)",{"$f":"42/300","v":0.14000000000000001},"±",{"$f":"_xlfn.T.INV(0.975,300-1)*SQRT(0.14*(1-0.14))/SQRT(300)","v":3.9424136463154319E-2},{"$f":"showformula(E41)","v":"=T.INV(0.975,300-1)*SQRT(0.14*(1-0.14))/SQRT(300)"},null,null,null,null,null,null,null,null,null,null," "]
[null,null,null,null,null,"(This will not be on your exam.)",null,null,null,null,null,null,null,null,null,null," "]
[]
[null,"8)",{"$f":"1-NORMDIST(0,C52,C53,TRUE)","v":0.81022225738715292},{"$f":"showformula(C44)","v":"=1-NORMDIST(0,C52,C53,TRUE)"},null,null,null,null,"﻿claim ","probability ",null,"profit","probability"]
[null,null,null,null,null,null,null,null,{"$f":"0","v":0},0.99,null,{"$f":"15-0","v":15},0.99]
[null,null,"If T is total profit then the expected value of T is",null,null,null,null,null,{"$f":"500","v":500},8.0000000000000002E-3,null,{"$f":"15-500","v":-485},8.0000000000000002E-3]
[null,null,"$40,000. The standard deviation of T is $45,520.98. By",null,null,null,null,null,{"$f":"5000","v":5000},2E-3,null,{"$f":"15-5000","v":-4985},2E-3]
[null,null,"the Central Limit Theorem, T will be approximately"]
[null,null,"normally distributed (since it is the sum of 40,000",null,null,null,null,null,{"$f":"SUMPRODUCT(I45:I47,J45:J47)","v":14},"E[claim]",{"$f":"showformula(I49)","v":"=SUMPRODUCT(I45:I47,J45:J47)"}]
[null,null,"independent random variables).",null,null,null,null,null,{"$f":"SQRT(SUMPRODUCT(I45:I47^2,J45:J47)-I49^2)","v":227.60492086068788},"StDev(claim)",{"$f":"showformula(I50)","v":"=SQRT(SUMPRODUCT(I45:I47^2,J45:J47)-I49^2)"}]
[null,null,null,null,null,null,null,null,{"$f":"SUMPRODUCT(L45:L47,M45:M47)","v":0.99999999999999822},"E[profit]",{"$f":"showformula(I51)","v":"=SUMPRODUCT(L45:L47,M45:M47)"}]
[null,null,{"$f":"40000*(15-I49)","v":40000},"E[T]",{"$f":"showformula(C52)","v":"=40000*(15-I49)"},null,null,null,{"$f":"SQRT(SUMPRODUCT(L45:L47^2,M45:M47)-I51^2)","v":227.60492086068791},"StDev(profit)",{"$f":"showformula(I52)","v":"=SQRT(SUMPRODUCT(L45:L47^2,M45:M47)-I51^2)"}]
[null,null,{"$f":"SQRT(40000)*I50","v":45520.984172137578},"StDev(T)",{"$f":"showformula(C53)","v":"=SQRT(40000)*I50"}]
[null,null,null,null,null,null,null,null,"(The $15 payment from everyone doesn't change the variability.)"]
[]
[null,"9)","There is a strong potential for sample bias in this case. It would depend on whether there is a"]
[null,null,"correlation between the size of a household and the likelihood that someone is home to"]
[null,null,"answer the door when an interviewer arrives. It may be reasonable to expect that these two"]
[null,null,"things are positively correlated: Larger households are more likely to have at least one"]
[null,null,"household member at home, and households with children could also be more likely to be at"]
[null,null,"home. By dismissing the observations for which no one is home, the School District may be"]
[null,null,"underrepresenting households with just one or two members. In this case, the District’s"]
[null,null,"household size estimate likely would be too high."]