8.4. 3. In a survey of 480 drivers from the​ South, 392 wear a seat belt. In a survey of 340 drivers from the​ Northeast, 293 wear a seat belt. At α=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 H0

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8.4. 3. In a survey of
480
drivers from the​ South,
392
wear a seat belt. In a survey of
340
drivers from the​ Northeast,
293
wear a seat belt. At
α=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
H0
and
Ha.
 
The claim is​ "the proportion of drivers who wear seat belts in the South is
(1) 
 
 
in the​ Northeast."
Let
p1
represent the population proportion for the​ South, and
p2
represent the population proportion for the Northeast. State
H0
and
Ha.
 
Choose the correct answer below.
 
 
A.
H0​:
p1=p2
Ha​:
p1≠p2
 
B.
H0​:
p1>p2
Ha​:
p1≤p2
 
C.
H0​:
p1<p2
Ha​:
p1≥p2
 
D.
H0​:
p1≠p2
Ha​:
p1=p2
 
E.
H0​:
p1≥p2
Ha​:
p1<p2
 
F.
H0​:
p1≤p2
Ha​:
p1>p2
​(b) Find the critical​ value(s) and identify the rejection​ region(s).
 
The critical​ value(s) is(are)
nothing.
​(Use a comma to separate answers as needed. Type an integer or a decimal. Round to two decimal places as​ needed.)
Identify the rejection​ region(s). Select the correct choice below and fill in the answer​ box(es) within your choice. ​(Round to two decimal places as​ needed.)
 
 
A.
z>
 
B.
z<
and
z>
 
C.
z<
 
D.
<z<
​(c) Find the standardized test statistic.
 
z=nothing
​(Round to two decimal places as​ needed.)
​(d) Decide whether to reject or fail to reject the null hypothesis.
 
Choose the correct answer below.
 
 
Fail to reject
H0
because the test statistic
is
in the rejection region.
 
Fail to reject
H0
because the test statistic
is not
in the rejection region.
 
Reject
H0
because the test statistic
is not
in the rejection region.
 
Reject
H0
because the test statistic
is
in the rejection region.
​(e) Interpret the decision in the context of the original claim.
 
Choose the correct answer below.
 
 
A.
At the
7​%
significance​ level, there is
sufficient
evidence to support the claim.
 
B.
At the
7​%
significance​ level, there is
insufficient
evidence to support the claim.
 
C.
At the
7​%
significance​ level, there is
insufficient
evidence to reject the claim.
 
D.
At the
7​%
significance​ level, there is
sufficient
evidence to reject the claim.
(1) 
 
 greater than
 
 different than
 
 less than
 
 the same as
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