A simple random sample of front-seat occupants involved in car crashes is obtained. Among2946occupants not wearing seat belts,31were killed. Among7602occupants wearing seat belts,16were killed. Use a0.01significance level to test the claim that seat belts are effective in reducing fatalities. Complete parts (a) through (c) below.

a.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.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

Identify the test statistic.

z = _________

(Round to two decimal places as needed.)

Identify the P-value.

P-value =_________

(Round to three decimal places as needed.)

What is the conclusion based on the hypothesis test

The P-value is (1)_________the significance level of = 0.01, so (2)_________the null hypothesis. There (3)_________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_________< p1 p2 <_________.

(Round to three decimal places as needed.)

What is the conclusion based on the confidence interval?

Because the confidence interval limits (4)_________0, it appears that the two fatality rates are (5)_________.

Because the confidence interval limits include (6) __________ values, it appears that the fatality rate is (7)_________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 the same fatality ratesas not using seat belts.

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

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

D. The results are inconclusive.

(1) less than

greater than

(2) reject

fail to reject

(3) is not

is

(4) include

do not include

(5) not equal.

equal.

(6) only positive

positive and negative

only negative

(7) lower

higher

the same