Question

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.

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. ( h_0: p_1
eq p_2 ), ( h_1: p_1 = p_2 )
b. ( h_0: p_1 = p_2 ), ( h_1: p_1lt p_2 )
c. ( h_0: p_1 = p_2 ), ( h_1: p_1gt p_2 )
d. ( h_0: p_1leq p_2 ), ( h_1: p_1
eq p_2 )
e. ( h_0: p_1 = p_2 ), ( h_1: p_1gt p_2 )
f. ( h_0: p_1geq p_2 ), ( h_1: p_1
eq p_2 )

Explanation:

We need to set up the null and alternative hypotheses for testing if seat belts are effective in reducing fatalities. Let \( p_1 \) be the proportion of fatalities among those not wearing seat belts and \( p_2 \) be the proportion among those wearing seat belts. The claim is that seat belts reduce fatalities, so \( p_1 > p_2 \) (since not wearing belts should have a higher fatality rate if belts are effective). The null hypothesis \( H_0 \) is a statement of equality, so \( H_0: p_1 = p_2 \), and the alternative hypothesis \( H_1 \) is what we want to support, so \( H_1: p_1 > p_2 \), which corresponds to option F.

Answer:

F. \( H_0: p_1 = p_2 \), \( H_1: p_1 > p_2 \)