Question

check 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: 0.000 (round to three decimal places as needed) what is the conclusion for this test? the p - value is \boxed{ } the significance level $\alpha$, so \boxed{ } the null hypothesis. there is \boxed{ } evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves? (a study: among 254 vinyl gloves, 62% leaked viruses. among 254 latex gloves, 6% leaked viruses. using a 0.05 significance level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves.)

Explanation:

Step 1: Identify Hypotheses

The claim is that vinyl gloves ( \( p_1 \)) have a greater virus leak rate than latex gloves ( \( p_2 \)). So null hypothesis \( H_0: p_1 = p_2 \), alternative \( H_1: p_1 > p_2 \), which matches option B.

Step 2: Test Statistic

Given test statistic is \( 13.31 \) (from the problem).

Step 3: P - value

Given P - value is \( 0.000 \) (rounded to three decimals).

Step 4: Conclusion

Since P - value (\( 0.000 \)) < significance level (\( \alpha = 0.05 \)), we reject \( H_0 \). There is sufficient evidence to support the claim.

Answer:

• Hypotheses: B. \( H_0: p_1 = p_2 \); \( H_1: p_1 > p_2 \)
• Test Statistic: \( 13.31 \)
• P - value: \( 0.000 \)
• Conclusion: Reject \( H_0 \); There is sufficient evidence.