Questions: 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 768 referee calls, and 224 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? A. H0 · p1 ≥ p2 B. H0: p1=p2 C. H0: p1=p2 H1: p1 ≠ p2 H3: p1 ≠ p2 H1: p1<p2 D. H0: P1=P2 E. H0: p1 ≠ p2 F. H0: p1 ≤ p2 H1: P1>P2 H1: p1=p2 H1: p1 ≠ p2

Solution Steps

We define the null and alternative hypotheses as follows:

• Null Hypothesis: \( H_0: p_1 = p_2 \) (men and women have equal success in challenging calls)
• Alternative Hypothesis: \( H_1: p_1 \neq p_2 \) (men and women do not have equal success in challenging calls)

The test statistic \( Z \) is calculated using the formula: \[ Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}} \] where:

• \( \hat{p} = \frac{411}{1422} \approx 0.2885 \) (sample proportion for men)
• \( p_0 = \frac{224}{768} \approx 0.2917 \) (hypothesized population proportion for women)
• \( n = 1422 \) (sample size for men)

Substituting the values, we find: \[ Z \approx -0.2188 \]

The P-value associated with the test statistic \( Z = -0.2188 \) is calculated to be: \[ \text{P-value} \approx 0.8268 \]

For a significance level of \( \alpha = 0.05 \) in a two-tailed test, the critical region is defined as: \[ Z < -1.96 \quad \text{or} \quad Z > 1.96 \]

Since the calculated P-value \( 0.8268 \) is greater than \( 0.05 \), we fail to reject the null hypothesis. This indicates that there is no significant difference in success rates between men and women in challenging calls.

Final Answer