Question

a newspaper published an article about a study in which researchers subjected laboratory gloves to stress. among 254 vinyl gloves, 62% leaked viruses. among 254 latex gloves, 6% leaked viruses. using the accompanying display of the technology results, and using a 0.05 significance level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves. let vinyl gloves be population 1. click the icon to view the technology results. what are the null and alternative hypotheses? a. $h_0: p_1 = p_2$ $h_1: p_1 \
eq p_2$ b. $h_0: p_1 > p_2$ $h_1: p_1 = p_2$ c. $h_0: p_1 = p_2$ $h_1: p_1 > p_2$ d. $h_0: p_1 \
eq p_2$ $h_1: p_1 = p_2$ e. $h_0: p_1 < p_2$ $h_1: p_1 = p_2$ f. $h_0: p_1 = p_2$ $h_1: p_1 < p_2$ identify the test statistic. 13.31 (round to two decimal places as needed.) identify the p - value. (round to three decimal places as needed.)

Explanation:

The problem is about testing the claim that vinyl gloves (population 1) have a greater virus leak rate than latex gloves (population 2). The null hypothesis \( H_0 \) assumes no difference (\( p_1 = p_2 \)), and the alternative hypothesis \( H_1 \) reflects the claim \( p_1 > p_2 \). Option C has \( H_0: p_1 = p_2 \) and \( H_1: p_1 > p_2 \), which matches the claim.

Answer:

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