Math  /  Data & Statistics

QuestionSince an instant replay system for tennis was introduced at a major tournament, men challenged 1384 referee calls, with the result that 431 of the calls were overturned. Women challenged 762 referee calls, and 212 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. H0:p1p2H_{0}: p_{1} \leq p_{2} B. H0:p1p2H_{0}: p_{1} \geq p_{2} C. H0:p1=p2H_{0}: p_{1}=p_{2} H1:p1p2H_{1}: p_{1} \neq p_{2} H1:p1p2H_{1}: p_{1} \neq p_{2} D. H0:p1=p2H_{0}: p_{1}=p_{2} E. H0:p1=p2H_{0}: p_{1}=p_{2} H1:p1<p2H_{1}: p_{1}<p_{2} H1:P1>P2H_{1}: P_{1}>P_{2} H1:p1p2H_{1}: p_{1} \neq p_{2} F. H0:p1p2H_{0}: p_{1} \neq p_{2} H1:p1=p2H_{1}: p_{1}=p_{2}

Studdy Solution
Conduct the hypothesis test.
- Calculate the sample proportions: - For men: p^1=4311384 \hat{p}_1 = \frac{431}{1384} - For women: p^2=212762 \hat{p}_2 = \frac{212}{762}
- Calculate the pooled sample proportion: $ \hat{p} = \frac{431 + 212}{1384 + 762} \]
- Calculate the standard error: $ SE = \sqrt{\hat{p}(1 - \hat{p}) \left( \frac{1}{1384} + \frac{1}{762} \right)} \]
- Calculate the test statistic: $ z = \frac{\hat{p}_1 - \hat{p}_2}{SE} \]
- Determine the critical value for a two-tailed test at α=0.01 \alpha = 0.01 .
- Compare the test statistic to the critical value to decide whether to reject the null hypothesis. (More calculations are needed for a complete test)
The null and alternative hypotheses are defined, and the correct option is identified as C. Further calculations are needed to complete the hypothesis test.

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