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 overtuned. 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.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
Also need test statistic & p-value
Since an instant replay system for tennis was introduced at a major tournament, men challenged 1,435 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.

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. \( H_0: p_1 = p_2 \)
       \( H_1: p_1 > p_2 \)

- B. \( H_0: p_1 \ge p_2 \)
       \( H_1: p_1 < p_2 \)

- 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. \( H_0: p_1 \le p_2 \)
       \( H_1: p_1 \neq p_2 \)

Identify the test statistic.

\( z = \) ______ 
(Round to two decimal places as needed.)

Identify the P-value.

P-value = ______ 
(Round to three decimal places as needed.)
Transcribed Image Text:Since an instant replay system for tennis was introduced at a major tournament, men challenged 1,435 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. 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. \( H_0: p_1 = p_2 \) \( H_1: p_1 > p_2 \) - B. \( H_0: p_1 \ge p_2 \) \( H_1: p_1 < p_2 \) - 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. \( H_0: p_1 \le p_2 \) \( H_1: p_1 \neq p_2 \) Identify the test statistic. \( z = \) ______ (Round to two decimal places as needed.) Identify the P-value. P-value = ______ (Round to three decimal places as needed.)
### Statistical Analysis Exercise: Evaluating Success in Challenging Tennis Calls

**Context:**
Since the introduction of an instant replay system for tennis at a major tournament, a study was conducted to test the claim that men and women have equal success in challenging referee calls. Men challenged 1,435 calls, and 427 were overturned. Women challenged 740 calls, with 218 overturned. The test uses a 0.01 significance level.

**Tasks & Analysis:**

#### a. Hypothesis Test Conclusion:
- Compare the P-value with the significance level (α = 0.01).
- Decision Making: Determine if there is enough evidence to reject the null hypothesis claiming equal success for men and women in challenges.

#### b. Confidence Interval Construction:
- Calculate the 99% confidence interval for the difference in proportion of successful challenges between men and women: \( (p_1 - p_2) \).
- Ensure that the interval is rounded to three decimal places.

#### Conclusion Based on Confidence Interval:
- Evaluate whether zero is within the confidence interval.
- If zero is outside the interval, there appears to be a significant difference between proportions, suggesting differences in success rates between men and women.

#### c. Evaluating Equal Success:
- Choose the correct conclusion from the following options:
  - **A.** No significant difference between the success of men and women.
  - **B.** Suggests men have more success.
  - **C.** Suggests women have more success.
  - **D.** Insufficient information for a conclusion.

This exercise involves interpreting statistical data to assess claims regarding gender differences in sports-related decision-making success. Use the results from hypothesis testing and confidence intervals to inform conclusions.
Transcribed Image Text:### Statistical Analysis Exercise: Evaluating Success in Challenging Tennis Calls **Context:** Since the introduction of an instant replay system for tennis at a major tournament, a study was conducted to test the claim that men and women have equal success in challenging referee calls. Men challenged 1,435 calls, and 427 were overturned. Women challenged 740 calls, with 218 overturned. The test uses a 0.01 significance level. **Tasks & Analysis:** #### a. Hypothesis Test Conclusion: - Compare the P-value with the significance level (α = 0.01). - Decision Making: Determine if there is enough evidence to reject the null hypothesis claiming equal success for men and women in challenges. #### b. Confidence Interval Construction: - Calculate the 99% confidence interval for the difference in proportion of successful challenges between men and women: \( (p_1 - p_2) \). - Ensure that the interval is rounded to three decimal places. #### Conclusion Based on Confidence Interval: - Evaluate whether zero is within the confidence interval. - If zero is outside the interval, there appears to be a significant difference between proportions, suggesting differences in success rates between men and women. #### c. Evaluating Equal Success: - Choose the correct conclusion from the following options: - **A.** No significant difference between the success of men and women. - **B.** Suggests men have more success. - **C.** Suggests women have more success. - **D.** Insufficient information for a conclusion. This exercise involves interpreting statistical data to assess claims regarding gender differences in sports-related decision-making success. Use the results from hypothesis testing and confidence intervals to inform conclusions.
Expert Solution
steps

Step by step

Solved in 5 steps

Blurred answer
Knowledge Booster
Basics of Inferential Statistics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman