8/18/2019 23932_Solution+Q2+finals

1/1

Solution: Quiz#2 Finals

1. Past experience indicates that the time for college sophomoresto complete a standardized placement test is normal randomvariable. sample of 2! students gave a mean time to completethe test of 2". min $ith standard deviation min.a. %sing & ' ! () test *o: + ' 2! min against *1: + , 2! min.b. Find the p-value for this test.c. hat assumptions must be made regarding the data for thetest in part /a0 to be valid

%se t-test

Problem reuire t$o-tailed test: &32 ' 4.42!5 df ' 2! 6 1 '2

t/tabulated0 ' 2.47

ith ´ x=25 5 t/computed0 ' |3|  8 t/table05 re9ect *o

ith t'5 p ' 4.4417"2 /&320 5 thus p ' 4.44

;ne can assume that the sample size is not representative of thesophomore population or there is the presence of outliers $hich$ere not considered.

2. ' 144 lb. *o$ large a sample must be chosen so that theprobabilit? the sample mean and the true mean di@er b? at most !lb is 4.A4

 P [|´ x− μ|≤5 lb ]≥0.90

 P(−5

s

√ n

≤  ´ x− μ

s

√ n

≤  5

s

√ n )≥0.90

Since itBs a t$o-tailed condition: & ' 14(5 &32 ' !(For p'4.A!5 z/table0 ' 1.7!