Question

A simple random sample of​ front-seat occupants involved in car crashes is obtained. Among 2720 occupants not wearing seat​ belts, 30 were killed. Among 7791 occupants wearing seat​ belts, 18 were killed. Use a 0.01 significance level to test the claim that seat belts are effective in reducing fatalities. Complete parts​ (a) through​ (c) below.

Test the claim using a hypothesis test.

Consider the first sample to be the sample of occupants not wearing seat belts and the second sample to be the sample of occupants wearing seat belts. What are the null and alternative hypotheses for the hypothesis​ test?

A.

Upper H 0H0​:

p 1p1not equals≠p 2p2

Upper H 1H1​:

p 1p1equals=p 2p2

B.

Upper H 0H0​:

p 1p1less than or equals≤p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

C.

Upper H 0H0​:

p 1p1greater than or equals≥p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

D.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1greater than>p 2p2

E.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1less than<p 2p2

F.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

Identify the test statistic.

zequals=nothing

​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-valueequals=nothing

​(Round to three decimal places as​ needed.)

What is the conclusion based on the hypothesis​ test?

The​ P-value is

▼

less than

greater than

the significance level of

alphaαequals=0.010.01​,

so

▼

fail to reject

reject

the null hypothesis. There

▼

is not

is

sufficient evidence to support the claim that the fatality rate is higher for those not wearing seat belts.

b. Test the claim by constructing an appropriate confidence interval.

The appropriate confidence interval is

nothingless than<left parenthesis p 1 minus p 2 right parenthesisp1−p2less than<nothing.

​(Round to three decimal places as​ needed.)

What is the conclusion based on the confidence​ interval?

Because the confidence interval limits

▼

do not include

include

​0, it appears that the two fatality rates are

▼

not equal.

equal.

Because the confidence interval limits include

▼

only negative

only positive

positive and negative

​values, it appears that the fatality rate is

▼

the same

lower

higher

for those not wearing seat belts.

c. What do the results suggest about the effectiveness of seat​ belts?

A.

The results suggest that the use of seat belts is associated with lower fatality rates than not using seat belts.

B.

The results suggest that the use of seat belts is associated with the same fatality rates as not using seat belts.

C.

The results suggest that the use of seat belts is associated with higher fatality rates than not using seat belts.

D.

The results are inconclusive.

Answer 1