Question

(round to two decimal places as needed )
identify the p - value.
p - value = 0.280
(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 = 0.05, 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 95% confidence interval is - 0.018 < (p₁ - p₂) < 0.062 (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 men have more success.
b. the confidence interval suggests that there is no significant difference between the success of men and women in challenging calls.
c. 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.
d. there is not enough information to reach a conclusion.

Explanation:

For part c, we analyze the confidence interval \(-0.018 < (p_1 - p_2) < 0.062\). Since the interval contains 0, this means there is no significant difference between the two proportions (success rates of men and women in challenging calls). So the confidence interval suggests no significant difference, and there's not enough evidence to say they differ. Option B states "The confidence interval suggests that there is no significant difference between the success of men and women in challenging calls" which matches this conclusion.

Answer:

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