Question #1 In1990, 5.8% ofjob applicants whowere testedfor drugsfailed thetest. A randomsample of1440currentjobapplicantsresults in61failures (basedloosely on datafromthe AmericanManagementAssociation).   Attheα=0.01significancelevel, testthebelowcl

Question #1

In1990, 5.8% ofjob applicants whowere testedfor drugsfailed thetest.

A randomsample of1440currentjobapplicantsresults in61failures (basedloosely on datafromthe AmericanManagementAssociation).

Attheα=0.01significancelevel, testthebelowclaim(i.e.,thatthefailure rateis now lower)

HO:p = 0.058

HA:p < 0.058

a) Is thisanuppertail,lower tail,or two-tailtest?(5points)

b) Are we testing meansor proportions?(5points)

c)Statethe rule ofrejection(in termsofp-valueandlevel ofsignificance) (5points)

d) Findthep-value(5points)

e) Shouldyourejector notreject HO?(5points)

f) Does theresult suggestthatfewer job applicantsnowuse drugs?(5 points)

Researchers studyinginfantheadcircumferences (incentimeters)wish totestifthe meanheadcircumference differsfromthehistorical mean of 34.5cm.Theresearchers obtainasample of17infantswithameanheadcircumference of34.16cmanda standard deviationof0.58cm.

Attheα=0.05significancelevel, testtheclaim

HO:µ=34.5

HA:µ≠ 34.5

a) Is thisanuppertail,lower tail,or two-tailtest?(5points)

b) Are we testing meansor proportions?(5points)

c)Statetherule ofrejection(in termsof p-valueandlevel ofsignificance) (5points)

d) Findthep-value(5points)

e) Shouldyourejector notreject HO?(5points)

f) Does theresult suggestthatthemeanheadcircumferencediffersfrom34.5cm? (5 points)

Question #3

Performthefollowing hypothesistest onthepaired data below:

HO:µd=0(Pleaserecallthat µdis read~and alsoknown as ~Mu-sub-d) HA:µd≠0Test atα=0.05

a) Isthisanuppertail,lower tail,or two-tailtest?(5points)

b) Are we testing meansor proportions? (5points)

c)Statetherule ofrejection(in termsofp-valueandlevel ofsignificance) (5points)

d) Findthep-value(5points)

e) Shouldyourejector notreject HO?(5points)

f) DothedataprovidesufficientevidencetosuggesttheAfter scores are indeed higher? Whyor whynot?(5points)

Note:Becausetheabove isatwo-tailtest,rejection ofHo aloneisnot a  sufficient reason.Hint: What elsedidyou observe among the sampleresults?