Since an instant replay system for tennis was introduced at a major tournament, men challenged 1407 referee calls, with the result that 414 of the calls were overturned. Women challenged 770 referee calls, and 224 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?

A. [tex]H_0: P_1 \leq P_2 \quad H_1: P_1 \neq P_2[/tex]

B.
[tex]H_0: p_1=p_2 \\\ \textless \ br/\ \textgreater \ H_1: p_1\ \textless \ p_2[/tex]

C. [tex]H_0: P_1=P_2 \quad H_1: P_1 \neq P_2[/tex]

D.
[tex]H_0: p_1=p_2 \\\ \textless \ br/\ \textgreater \ H_1: p_1\ \textgreater \ p_2[/tex]

E.
[tex]H_0: P_1 \neq P_2 \\\ \textless \ br/\ \textgreater \ H_1: P_1 = P_2[/tex]

F. [tex]H_0: P_1 \geq P_2 \quad H_1: P_1 \neq P_2[/tex]

### Identify the test statistic.
[tex]z=0.16[/tex]
(Round to two decimal places as needed.)

### Identify the [tex]P[/tex]-value.
[tex]P\text{-value}=0.87[/tex]
(Round to three decimal places as needed.)

### What is the conclusion based on the hypothesis test?
The [tex]P[/tex]-value is greater than the significance level of [tex]\alpha=0.01[/tex], so we fail to reject the null hypothesis. There is insufficient evidence to warrant rejection of the claim that women and men have equal success in challenging calls.

### Step-by-Step Solution:

Let's go through each part of the problem:

#### Part (a): State the Hypotheses
We need to test the claim that men and women have equal success in challenging referee calls.

- Null Hypothesis ([tex]\(H_0\)[/tex]): The success rate of men and women in challenging calls is equal. Mathematically, this can be represented as [tex]\(H_0: p_1 = p_2\)[/tex].
- Alternative Hypothesis ([tex]\(H_1\)[/tex]): The success rate of men and women in challenging calls is not equal. This can be represented as [tex]\(H_1: p_1 \neq p_2\)[/tex].

Given these options, the correct hypothesis statements are:
[tex]\[ C. \, H_0: p_1 = p_2 \, \text{and} \, H_1: p_1 \neq p_2 \][/tex]

#### Part (b): Identify the Test Statistic
We calculate the test statistic, which is [tex]\(z\)[/tex].

Given:
[tex]\[ z = 0.16 \][/tex]

This is rounded to two decimal places.

#### Part (c): Identify the [tex]\(P\)[/tex]-value
We use the test statistic to find the [tex]\(P\)[/tex]-value, which helps us decide whether to reject the null hypothesis or not.

Given:
[tex]\[ P\text{-value} = 0.87 \][/tex]

This is rounded to three decimal places.

#### Part (d): Conclusion Based on the Hypothesis Test
To conclude, we compare the [tex]\(P\)[/tex]-value with the significance level ([tex]\(\alpha = 0.01\)[/tex]):

- If [tex]\(P\)[/tex]-value [tex]\( \leq \alpha \)[/tex], we reject the null hypothesis.
- If [tex]\(P\)[/tex]-value [tex]\( > \alpha \)[/tex], we fail to reject the null hypothesis.

Given:
[tex]\[ P\text{-value} = 0.87 > 0.01 \][/tex]

Since the [tex]\(P\)[/tex]-value is greater than the significance level ([tex]\(\alpha = 0.01\)[/tex]), we fail to reject the null hypothesis.

Therefore, we conclude that there is not enough evidence to warrant rejection of the claim that men and women have equal success in challenging referee calls.

### Final Conclusion
Completing the last part in the text:

"The [tex]\(P\)[/tex]-value is greater than the significance level of [tex]\(\alpha = 0.01\)[/tex], so we fail to reject the null hypothesis. There is not enough evidence to warrant rejection of the claim that women and men have equal success in challenging calls."