Question

A state's Division of Motor Vehicles (DMV) claims that 60% of teens pass their driving test on the first attempt. An investigative reporter examines an SRS of the DMV records for 125 teens; 56 of them passed the test on their first try. Is there convincing evidence at the α=0.01 significance level that the DMV's claim is lower?

Answer 1

null Hypothesis:               Ho:   p		=	0.600
alternate Hypothesis:    Ha: p		<	0.600
for 0.01 level with left tailed test , critical z=			-2.33
Decision rule :   reject Ho if test statistic z < 2.326
sample success x   =		56
sample size          n    =		125
std error   se =√(p*(1-p)/n) =		0.0438
sample proportion p̂ = x/n=		0.4480
test stat z =(p̂-p)/√(p(1-p)/n)=		-3.47

since test statistic falls in rejection region we reject null hypothesis
we have sufficient evidence to conclude that the DMV's claim is lower