Question

Since an instant replay system for tennis was introduced at a major​ tournament, men challenged 1424 referee​ calls, with the result that 424 of the calls were overturned. Women challenged 750 referee​ calls, and 221 of the calls were overturned. Use a 0.01 significance level to test the claim that men and women have equal success in challenging calls. Complete parts​ (a) through​ (c) below.

a. Test the claim using a hypothesis test.

Consider the first sample to be the sample of male tennis players who challenged referee calls and the second sample to be the sample of female tennis players who challenged referee calls. What are the null and alternative hypotheses for the hypothesis​ test?

Identify the test statistic.

z = ____

​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-value = ______

​(Round to three decimal places as​ needed.)

What is the conclusion based on the hypothesis​ test?

The​ P-value is (less than or greater than) the significance level of α = 0.01 , so (fail to reject or reject) the null hypothesis. There (is sufficient or 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 ___ < (p₁-p₂) < ___

​(Round to three decimal places as​ needed.)

What is the conclusion based on the confidence​ interval?

Because the confidence interval limits (include or do not include) ​0, there (does not or does) appear to be a significant difference between the two proportions. There (is not sufficient or is 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 no significant difference between the success of men and women in challenging calls.

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 women have more success.

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 men have more success.

D.There is not enough information to reach a conclusion.

Answer 1