Anexperiment40 used asampleofcollegestudentstoinvestigatewhethercellphoneuseimpairs drivers’reactiontimes.Onamachinethatsimulateddrivingsituations,atirregularperiods a targetflashedredorgreen.Participantswereinstructedtopressabrakebuttonassoonas possiblewhentheydetectedaredlight.Underthecellphonecondition,eachstudentcarried out aconversationonacellphonewithsomeoneinaseparateroom.Inthecontrolcondition, the samestudentslistenedtoaradiobroadcast.The CellPhone data filerecordsthestudents’

mean responsetimes(inmilliseconds)overseveraltrialsforeachcondition, {yi1} for thecell phone conditionand {yi2} for control.

(a) Thecomparisonsofmeansorproportionsinthischapterassumeindependentsamplesfor the twogroups.Explainwhythesamplesforthesetwoconditionsare dependent rather than independent.

(b) Tocompare μ1 and μ2, youcanuse {di = yi1 − yi2, i = 1, ...,n}, herewith n = 8. Specify the parameter μd and H0 for doingthis,andexplainwhy μd = μ1 − μ2.

(c) Statetheassumptionsandteststatistic,explainwhyithasa t distribution with df = n−1.

Reportthe P-valuewithtwo-sided Ha, andinterpret.(Thetestiscalleda matched-pairs t test. Matched-pairsanalysesalsoarepossiblewithconfidenceintervals,as Section 4.4.3 did incomparingweightsofanorexicgirlsbeforeandafteraperiodoftreatmentby analyzing themeandifferenceinweights.)