Question

4.) Since an instant replay system for tennis was introduced at a major​ tournament, men challenged 1422 referee​ calls, with the result that 411 of the calls were overturned. Women challenged 771 referee​ calls, and 228 of the calls were overturned. Use a 0.05 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?

a1) Identify the test statistic (Round to two decimal places as needed)

a2) Identify the P Value (Round to three decimal places as needed)

a3) What is the conclusion based on the hypothesis test?

b) Test the claim by constructing an appropriate confidence level. (Round to three decimal places as needed)

b1) What is the conclusion based on the confidence interval?

Because the confidence interval limits _____ (include/does not include) 0, there _____(does/does not) appear to be a significant difference between the two proportions. There is _______(sufficient/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 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

We are asked to perform difference between 2 sample proportion test and interval.

Let x₁ be the number of male tennis players who challenged referee calls got overturned : 411

n₁ be the number of male tennis players who challenged referee calls : 1422

x₂ be the number of female tennis players who challenged referee calls got overturned : 228

n₂ be the number of female tennis players who challenged referee calls : 771

null and alternative hypotheses :

H₀ : P₁ = P₂ vs Ha : P₁ ≠ P₂

We can use TI-84 calculator to perform the test.

Press STAT key ---> Scroll to TESTS ----> Scroll to 2-prop z test and hit enter.

Plug the given values accordingly , select sign under H_a , then scroll to calculate and hit enter.

a1) test statistic =  -0.33

a2) Identify the P Value = 0.742

a3) conclusion based on the hypothesis test :

As p -value is greater than 0.05 , we fail to reject H₀, So there is no significant evidence to warrant rejection of the claim that men and women have equal success in challenging calls.

b) confidence level = 1 - 0.05 = 0.95 .

We can use TI-84 calculator .

Press STAT key ---> Scroll to TESTS ----> Scroll to 2-prop z Interval and hit enter.

Plug the given values accordingly and scroll to calculate, hit enter.

So confidence interval is ( - 0.047 , 0.033 )

b1)

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