Question

A simple random sample of​ front-seat occupants involved in car crashes is obtained. Among 2719 occupants not wearing seat​ belts, 39 were killed. Among 7860 occupants wearing seat​ belts, 19 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?

A. H0​: p 1 > or = p2

H1​: p 1 ≠ p2

B. H0​: p 1 ≥ p2

H1​: p 1p ≠ p2

C. H0​: p 1 = p2

H1​: p 1 < p2

D. H0​: p 1 ≠ p2

H1​: p 1 = p2

E. H0​: p 1 = p2

H1​: p 1 ≠ p2

F. H0​: p 1 = p2

H1​:p 1p > 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▼(less than, greater than) the significance level of α = 0.05​, so ▼(reject, fail to 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 ???<l(p1-p2)<???.

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

What is the conclusion based on the confidence​ interval?

Because the confidence interval limits ▼(include, do not include) ​0, it appears that the two fatality rates are ▼(not equal., equal.) Because the confidence interval limits include ▼(only positive, positive and negative, only negative) values, it appears that the fatality rate is ▼(lower, the same) 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 higher fatality rates than not using seat belts.

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

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

D. The results are inconclusive.

2.

Listed below are systolic blood pressure measurements​ (mm Hg) taken from the right and left arms of the same woman. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Use a 0.01significance level to test for a difference between the measurements from the two arms. What can be​ concluded?

Right arm	147	136	141	133	132
Left arm	172	168	191	155	151

In this​ example, μd is the mean value of the differences d for the population of all pairs of​ data, where each individual difference d is defined as the measurement from the right arm minus the measurement from the left arm. What are the null and alternative hypotheses for the hypothesis​ test?

A. H0​: μd ≠ 0

H1​: μd > 0

B. H0​: μd = 0

H1​: μd < 0

C.H0​:μd = 0

H1​: dμ ≠ 0

D. H0​:μd ≠ 0

H1​:μd = 0

Identify the test statistic.

t = ??? ​(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?

Since the​ P-value is ▼(less, greater) than the significance​ level, ▼(fail to reject, reject) the null hypothesis. There ▼(is not, is) sufficient evidence to support the claim of a difference in measurements between the two arms.

Answer 1

1)

a)