Question

A simple random sample of​ front-seat occupants involved in car crashes is obtained. Among 2992 occupants not wearing seat​ belts, 33 were killed. Among 7871 occupants wearing seat​ belts,13 were killed. Use a 0.05 significance 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?

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 (less than or greater than) the significance level of α =0.05​, so (reject or fail to reject) the null hypothesis. There (is or is not) 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 (do not include or include) 0, it appears that the two fatality rates are (equal or not equal. Because the confidence interval limits include (only negative or positive and negative or only positive) values, it appears that the fatality rate is (lower or the same or 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 the same fatality rates as not using seat belts.

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

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

D. The results are inconclusive.

Answer 1