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A simple random sample of​ front-seat occupants involved incar crashes is obtained. Among
2944
occupants not wearing seat​ belts,
37
were killed. Among
7774
occupants wearing seat​ belts,
17
were killed. Use a
0.05
significance level to test the claim that seat belts areeffective in reducing fatalities. Complete parts​ (a)through​ (c) below.
Question content area bottom
Part 1
a. Test the claim using a hypothesis test.
Consider the first sample to be the sample of occupants notwearing seat belts and the second sample to be the sample ofoccupants wearing seat belts. What are the null and alternativehypotheses for the hypothesis​ test?
A.
H0​:
p1≥p2
H1​:
p1≠p2
B.
H0​:
p1=p2
H1​:
p1≠p2
C.
H0​:
p1=p2
H1​:
p1<p2
D.
H0​:
p1≤p2
H1​:
p1≠p2
E.
H0​:
p1≠p2
H1​:
p1=p2
F.
H0​:
p1=p2
H1​:
p1>p2
Part 2
Identify the test statistic.
z=enter your response here
​(Round to two decimal places as​ needed.)
Part 3
Identify the​ P-value.
​P-value=enter your response here
​(Round to three decimal places as​ needed.)
Part 4
What is the conclusion based on the hypothesis​ test?
The​ P-value is
▼
greater than
less than
the significance level of
α=0.05​,
so
▼
fail to reject
reject
the null hypothesis. There
▼
is not
is
sufficient evidence to support the claim that the fatality rateis higher for those not wearing seat belts.
Part 5
b. Test the claim by constructing an appropriate confidenceinterval.
The appropriate confidence interval is
enter your response here<p1−p2<enter your responsehere.
​(Round to three decimal places as​ needed.)
Part 6
What is the conclusion based on theconfidence​ interval?
Because the confidence interval limits
▼
include
do not include
​0, it appears that the two fatality rates are
▼
equal.
not equal.
Because the confidence interval limits include
▼
positive and negative
only negative
only positive
​values, it appears that the fatality rate is
▼
lower
higher
the same
for those not wearing seat belts.
Part 7
c. What do the results suggest about the effectiveness ofseat​ belts?
A.
The results suggest that the use of seat belts is associatedwith higher fatality rates than not using seat belts.
B.
The results suggest that the use of seat belts is associatedwith the same fatality rates as not using seat belts.
C.
The results suggest that the use of seat belts is associatedwith lower fatality rates than not using seat belts.
D.
The results are inconclusive.