(1) In a sample of 200 adult drivers, 40% admitted that they often use their cel
ID: 3054818 • Letter: #
Question
(1) In a sample of 200 adult drivers, 40% admitted that they often use their cell phone while driving. In a sample of 220 adolescent drivers, 32% admitted that they often use their cell phone while driving (a) Find the 90% confidence interval for the difference in the proportions of adult and adolescent drivers who use their phone while driving. (b) Test whether the proportion of adult drivers who often use their cell phone while driving is actualy higher than the proportion of adolescents who do the same, using a 10% level of significance.Explanation / Answer
p = (p1 * n1 + p2 * n2) / (n1 + n2)
n1=200,p1=0.4
n2=220,p2=0.32
p=(0.4*200+0.32*220)/420=0.35
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
where p is the pooled sample proportion, n1 is the size of sample 1, and n2 is the size of sample 2.
=sqrt(0.35*(1-0.35)*((1/200)+(1/220)))
= 0.0466
90% CI for the difference in the proportions
=(p1-p2)+/-Zalpha/2* Standard error
=0.08+/-1.64*0.0466
90% CI =(0.003576, 0.156424)
B) We have to test
H0:p1=p2
H1=p1>p2
Test statistic. The test statistic is a z-score (z) defined by the following equation.
z = (p1 - p2) / SE
=0.08/0.0466
=1.716738
p-Value is p(Z>1.716738)=0.04 less than 0.05 Hence we reject H0 at 10 % los
Hence proportion of adult driver who use cell phone higher than adolescents who do the same
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