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. $h_0: p_1 = p_2$ $h_1: p_1 < p_2$

Explanation:

To determine the null and alternative hypotheses, we analyze the claim: "vinyl gloves have a greater virus leak rate than latex gloves". Let \( p_1 \) be the virus leak rate for vinyl gloves (population 1) and \( p_2 \) for latex gloves (population 2).

• Null Hypothesis (\( H_0 \)): Represents the status quo or no difference. For a claim about \( p_1 > p_2 \), the null hypothesis assumes equality: \( H_0: p_1 = p_2 \).
• Alternative Hypothesis (\( H_1 \)): Reflects the claim. The claim is \( p_1 > p_2 \), so \( H_1: p_1 > p_2 \).

Now, match with the options:

• Option C: \( H_0: p_1 = p_2 \), \( H_1: p_1 > p_2 \) matches the derived hypotheses.

Answer:

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