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 ) technology results pooled proportion: 0.34 test statistic: ( z = 13.3133 ) critical ( z = 1.6449 ) p - value: 0.0000 90% confidence interval: ( 0.5033215 < p_1 - p_2 < 0.6147887 ) print done

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 \(H_0\) for a two - proportion test of a greater - than claim is that the proportions are equal (\(p_1 = p_2\)), and the alternative hypothesis \(H_1\) is that \(p_1>p_2\) (since we are testing if vinyl has a greater leak rate). Looking at the options, option B has \(H_0:p_1 = p_2\) and \(H_1:p_1>p_2\) which matches our reasoning.

Answer:

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