MATLAB: An Introduction with Applications
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ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Based on the results, does it appear that men and women may have equal success in challenging calls?
Transcribed Image Text:**Hypothesis Testing in Tennis Tournament - Educational Example**
**Context:**
An instant replay system in tennis was introduced at a major tournament. In this event:
- Men challenged 1435 referee calls.
- Women challenged 740 referee calls.
- Out of these, 427 calls were overturned for men, and for women, 218 calls were overturned.
The objective is to test at a 0.01 significance level whether men and women have equal success rates in challenging calls.
**Hypothesis Testing:**
**Task:** Test the claim using a hypothesis test.
**Considerations:**
- First sample: Male tennis players challenging referee calls.
- Second sample: Female tennis players challenging referee calls.
**Objective:** Identify the null and alternative hypotheses for the hypothesis test.
**Options for Null (\( H_0 \)) and Alternative (\( H_1 \)) Hypotheses:**
- **A.** \( H_0: p_1 = p_2 \); \( H_1: p_1 > p_2 \)
- **B.** \( H_0: p_1 \geq p_2 \); \( H_1: p_1 \neq p_2 \)
- **C.** \( H_0: p_1 \neq p_2 \); \( H_1: p_1 = p_2 \)
- **D.** \( H_0: p_1 = p_2 \); \( H_1: p_1 < p_2 \)
- **E.** \( H_0: p_1 = p_2 \); \( H_1: p_1 \neq p_2 \)
- **F.** \( H_0: p_1 \leq p_2 \); \( H_1: p_1 \neq p_2 \)
**Statistical Analysis:**
**Identify the Test Statistic:**
- Calculate the test statistic (z-score) and round it to two decimal places.
**Identify the P-value:**
- Determine the P-value based on the calculated z-score.
This setup provides a structured format to guide students in formulating hypotheses and analyzing data for hypothesis testing in a real-world scenario.
![**Title: Statistical Analysis of Tennis Challenge Success Rates**
Since an instant replay system for tennis was introduced at a major tournament, men challenged 1435 referee calls, with the result that 427 of the calls were overturned. Women challenged 740 referee calls, and 218 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.
**Part (a): Hypothesis Test**
1. **Identify the Test Statistic:**
- \( z = \) [Box for input]
*(Round to two decimal places as needed)*
2. **Identify the P-value:**
- \( P\text{-value} = \) [Box for input]
*(Round to three decimal places as needed)*
3. **Conclusion Based on the Hypothesis Test:**
- The P-value is [Dropdown selection] the significance level of \( \alpha = 0.01 \), so [Dropdown selection] the null hypothesis. There [Dropdown selection] evidence to warrant rejection of the claim that women and men have equal success in challenging calls.
**Part (b): Confidence Interval**
- Test the claim by constructing an appropriate confidence interval. [Instructions for where to input the confidence interval calculations]
*Note: Students should ensure they understand how to compute the test statistic and the P-value accurately. Familiarity with hypothesis testing and confidence intervals is crucial for this exercise.*](https://content.bartleby.com/qna-images/question/3c4a10a4-f78a-4b33-baf7-d4cbff942cfa/9aabc6ba-7dc4-4b01-a394-667122de838e/q8ukv4e_processed.jpeg)
Transcribed Image Text:**Title: Statistical Analysis of Tennis Challenge Success Rates**
Since an instant replay system for tennis was introduced at a major tournament, men challenged 1435 referee calls, with the result that 427 of the calls were overturned. Women challenged 740 referee calls, and 218 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.
**Part (a): Hypothesis Test**
1. **Identify the Test Statistic:**
- \( z = \) [Box for input]
*(Round to two decimal places as needed)*
2. **Identify the P-value:**
- \( P\text{-value} = \) [Box for input]
*(Round to three decimal places as needed)*
3. **Conclusion Based on the Hypothesis Test:**
- The P-value is [Dropdown selection] the significance level of \( \alpha = 0.01 \), so [Dropdown selection] the null hypothesis. There [Dropdown selection] evidence to warrant rejection of the claim that women and men have equal success in challenging calls.
**Part (b): Confidence Interval**
- Test the claim by constructing an appropriate confidence interval. [Instructions for where to input the confidence interval calculations]
*Note: Students should ensure they understand how to compute the test statistic and the P-value accurately. Familiarity with hypothesis testing and confidence intervals is crucial for this exercise.*
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