Question

homework
question 5, 9.1.13-t
part 7 of 7
hw score: 71.25%, 5.7 of 8 points
points: 0 of 1
a simple random sample of front-seat occupants involved in car crashes is obtained. among 2765 occupants not wearing seat belts, 31 were killed. among 7891 occupants wearing seat belts, 12 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.
(round to two decimal places as needed )
identify the p - value
p - value = 0
(round to three decimal places as needed )
what is the conclusion based on the hypothesis test?
the p - value is less than the significance level of α = 0.05, so reject the null hypothesis. there 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 0.006 < (p₁ - p₂) < 0.013 (round to three decimal places as needed )
what is the conclusion based on the confidence interval?
because the confidence interval limits do not include 0, it appears that the two fatality rates are not equal. because the confidence interval limits include only positive values, it appears that the fatality rate is 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.

Explanation:

For part (c), we analyze the confidence interval for \((p_1 - p_2)\) which is \(0.0006 < (p_1 - p_2) < 0.0013\). Here, \(p_1\) is the fatality rate for non - seat - belt users and \(p_2\) is for seat - belt users. Since the entire confidence interval is positive, it means \(p_1 - p_2>0\) or \(p_1 > p_2\). So the fatality rate for those not wearing seat belts ( \(p_1\)) is higher than for those wearing seat belts ( \(p_2\)), which implies that using seat belts is associated with lower fatality rates. Option A states "The results suggest that the use of seat belts is associated with lower fatality rates than not using seat belts" which matches our analysis. Option B is wrong as the interval doesn't suggest equal rates. Option C is wrong as the interval shows \(p_1>p_2\) not the opposite. Option D is wrong as the interval is conclusive.

Answer:

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