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Lecture 5

# STA 205 Lecture Notes - Lecture 5: Confidence IntervalExam

Department
Statistics
Course Code
STA 205
Professor
Brooke Buckley
Lecture
5

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12/17/2018 NKU Imath Assessment
https://imath.nku.edu/course/gb-viewasid.php?stu=11461&cid=335&asid=149931&uid=11461 1/7
Damico , Emily
Topic 5: Confidence Interval for the Proportion
Started: October 1, 2018, 12:45 pm
Last change: October 1, 2018, 4:59 pm
Total time questions were on‑screen: 139.1 minutes.
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Mobiletechnologyhaschangedthewayconsumersaccessinformationandentertainment.In2014,itwas
reportedthat47.8%ofsmartphoneusersbetweentheagesof18and29regularlyusetheirsmartphoneto
watchmoviesorTVthroughapaidsubscriptionservice(suchasNetflixorHulu).ThePewResearch
Organizationundertookastudytoseeifthispercentagehaschangedinthelastyear.Arandomsampleof
279smartphoneusersinthisagerangewasselected,anditwasfoundthat147ofthosesampledusetheir
smartphonetowatchmoviesorTVthroughapaidsubscriptionservice.Testtheappropriatehypotheses
usingasignificancelevelof0.10.
    
= decisionrule:reject ifprobability  
TestStatistic:z= (Note:roundthezscoretotwodecimalplacescarryatleastfourdecimal
placesthroughoutallofyourcalculations)
probability= (Note:roundtheprobabilitytofourdecimalplaces)
decision: 
Conclusion:Atthe0.10level,there  significantevidencetoconcludethe
percentageofsmartphoneusersbetweentheagesof18&29whoregularlyusetheirsmartphonesto
watchmoviesorTVthroughapaidserviceis than47.8%.
Question 1: 7.5 (parts: 0.25, 0.5, 0.25, 0.25, 0.5, 0.25, 0.5, 0.5, 2.5, 0, 0.45, 1, 0.5) out of 10 (parts: 0.25,
0.5, 0.25, 0.25, 0.5, 0.25, 0.5, 0.5, 2.5, 2.5, 0.5, 1, 0.5)in 3 attempt(s)

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12/17/2018 NKU Imath Assessment
https://imath.nku.edu/course/gb-viewasid.php?stu=11461&cid=335&asid=149931&uid=11461 2/7
Supposethefollowinghypothesesaretested: versus
Whatistheappropriatedecisionruleforthistest?
reject ifprobability<
reject ifprobability
reject ifprobability>
Theprobabilityforthetestisfoundtobe0.1209.Basedonthedecisionruleabove,whattypeoferroris
possibleif =0.05?
TypeIerror
TypeIIerror
Ifthesignificancelevelwerechangedto =0.10,whateffectwouldithaveontheerrorabove?
ATypeIerrorwouldnowbepossible.
ATypeIIerrorwouldnowbepossible.
Therewouldbenochangeinerror.
Question 2: 5.8 (parts: 2, 2, 1.8) out of 6 (parts: 2, 2, 2)in 3 attempt(s)
Ifthelevelofconfidenceincreases,theconfidenceinterval:
staysthesame
getswider
getsnarrower