Question

(round to two decimal places as needed)
identify the p - value.
p - value = 0.238
(round to three decimal places as needed)
what is the conclusion based on the hypothesis test?
the p - value is greater than the significance level of α = 0.01, so fail to reject the null hypothesis. there is not sufficient evidence to warrant rejection of the claim that women and men have equal success in challenging calls.
b. test the claim by constructing an appropriate confidence interval.
the 99% confidence interval is - 0.028 < (p₁ - p₂) < 0.076 (round to three decimal places as needed)
what is the conclusion based on the confidence interval?
because the confidence interval limits include 0, there does not appear to be a significant difference between the two proportions. there is not sufficient evidence to warrant rejection of the claim that men and women have equal success in challenging calls.
c. based on the results, does it appear that men and women may have equal success in challenging calls?
a. the confidence interval suggests that there is a significant difference between the success of men and women in challenging calls. it is reasonable to speculate that women have more success.
b. the confidence interval suggests that there is a significant difference between the success of men and women in challenging calls. it is reasonable to speculate that men have more success.
c. the confidence interval suggests that there is no significant difference between the success of men and women in challenging calls.
d. there is not enough information to reach a conclusion.

Explanation:

Part c: Analyzing the Confidence Interval

To determine if men and women have equal success in challenging calls, we analyze the 99% confidence interval for \((p_1 - p_2)\), which is \(-0.028 < (p_1 - p_2) < 0.076\).

• A confidence interval containing \(0\) implies there is no significant difference between the two proportions (since \(p_1 - p_2 = 0\) means equal success rates).
• The interval here includes \(0\), so we cannot conclude a significant difference. However, the interval’s upper bound is positive (\(0.076\)) and lower bound is negative (\(-0.028\)), suggesting the difference could favor either group, but the overlap with \(0\) means we lack sufficient evidence to reject the claim of equal success.

Final Answers

Part c:

The 99% confidence interval for \((p_1 - p_2)\) is \(-0.028 < (p_1 - p_2) < 0.076\), which includes \(0\). This means there is no significant difference between the success rates of men and women, and we cannot conclude one group has more success. Option C states the interval suggests no significant difference, which matches.

Answer:

C. The confidence interval suggests that there is no significant difference between the success of men and women in challenging calls.