Question

In a survey of 490 drivers from the South, 412 wear a seat belt. In a survey of 350 drivers from the Northeast, 291 wear a seat belt. At 0.07, can you support the claim that the proportion of drivers who wear seat belts is greater in the South than in the Northeast? Assume the random samples are independent. Complete parts (a) through (e) (a) Identify the claim and state Ho and H The claim is the proportion of drivers who wear seat belts in the South is in the Northeast."

Answer 1

a)

null Hypothesis:    Ho:    p1-p2		=	0.00
alternate Hypothesis: Ha:   p1-p2		>	0.00

The claim is the proportion of drivers who wear seat belts in the South is creat in the Northeast."

(below are detail of test):

for 0.07 level with right tailed test , critical value of z=			1.48
Decision rule :                   reject Ho if test statistic z > 1.476
	South		Northeast
x1                =	412	x2                =	291
p̂1=x1/n1 =	0.8408	p̂2=x2/n2 =	0.8314
n1                       =	490	n2                       =	350
estimated prop. diff =p̂1-p̂2    =		0.0094
pooled prop p̂ =(x1+x2)/(n1+n2)=		0.8369
std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =		0.0259
test stat z=(p̂1-p̂2)/Se =		0.3631
P value   =		0.3583

(please reply if further help is required on this)