Question

Testing the Difference Between Two Proportions. In Exercises 7–12, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent.

11. Seat Belt Use In a survey of 1000 drivers from the West, 934 wear a seat belt. In a survey of 1000 drivers from the Northeast, 909 wear a seat belt. At a = 0.05, can you support the claim that the proportion of drivers who wear seat belts is greater in the West than in the Northeast?

Answer 1

7.

Given that,
sample one, x1 =934, n1 =1000, p1= x1/n1=0.934
sample two, x2 =909, n2 =1000, p2= x2/n2=0.909
null, Ho: p1 = p2
alternate, H1: p1 > p2
level of significance, α = 0.05
from standard normal table,right tailed z α/2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = (p1-p2)/√(p^q^(1/n1+1/n2))
zo =(0.934-0.909)/sqrt((0.922*0.079(1/1000+1/1000))
zo =2.078
| zo | =2.078
critical value
the value of |z α| at los 0.05% is 1.645
we got |zo| =2.078 & | z α | =1.645
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value: right tail - Ha : ( p > 2.0785 ) = 0.01883
hence value of p0.05 > 0.01883,here we reject Ho
ANSWERS
---------------
a.
null, Ho: p1 = p2
alternate, H1: p1 > p2
c.
test statistic: 2.078
b.
critical value: 1.645
d.
decision: reject Ho
p-value: 0.01883
e.
we have enough evidence to support the claim that the proportion of drivers who wear seat belts is greater in the West than in the Northeast.