Since an instant replay system for tennis was introduced at a major tournament, men challenged 1402 referee calls, with the result that 418 of the calls were overturned. Women challenged 765 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 hypothesis test? female tennis players who challenged referee calls. What are the null and alternative hypotheses for the O A. Ho: P1 =P2 H: P P2 O D. Ho: P, 2 p2 H:P, *P2 OE. Ho: P, SP2 H: P1 P2 OF. Ho: P, #P2 H: P, "P2 Identify the test statistic. (Round to two decimal places as needed.) Identify the P-value. P-value =O (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? The P-value is V the significance level of a = 0.01, so the null hypothesis. There v evidence warrant rejection of the claim that women and men have equal success in challenging calls. b. Test the claim by constructing an appropriate confidence interval. The 99% confidence interval is < (P, - P2)

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Since an instant replay system for tennis was introduced at a major tournament, men challenged 1402 referee calls, with 418 of the calls being overturned. Women challenged 765 referee calls, and 212 calls were overturned. Using a 0.01 significance level, 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.** \( H_0: p_1 = p_2 \)  
  \( H_1: p_1 \neq p_2 \)

- **C.** \( H_0: p_1 = p_2 \)  
  \( H_1: p_1 > p_2 \)

- **D.** \( H_0: p_1 \neq p_2 \)  
  \( H_1: p_1 = p_2 \)

- **E.** \( H_0: p_1 \leq p_2 \)  
  \( H_1: p_1 \neq p_2 \)

- **F.** \( H_0: p_1 \neq p_2 \)  
  \( H_1: p_1 = p_2 \)

**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.)

**What is the conclusion based on the hypothesis test?**

The P-value is \( \) the significance level of \( \alpha = 0.01 \), so \( \) the null hypothesis. There \( \) evidence to warrant rejection of the claim that women and men have equal success in challenging calls.

**b. Test the claim by constructing an appropriate confidence interval:**

The 99% confidence interval is \( < (p_1 - p_2) < \) (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 1402 referee calls, with 418 of the calls being overturned. Women challenged 765 referee calls, and 212 calls were overturned. Using a 0.01 significance level, 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.** \( H_0: p_1 = p_2 \) \( H_1: p_1 \neq p_2 \) - **C.** \( H_0: p_1 = p_2 \) \( H_1: p_1 > p_2 \) - **D.** \( H_0: p_1 \neq p_2 \) \( H_1: p_1 = p_2 \) - **E.** \( H_0: p_1 \leq p_2 \) \( H_1: p_1 \neq p_2 \) - **F.** \( H_0: p_1 \neq p_2 \) \( H_1: p_1 = p_2 \) **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.) **What is the conclusion based on the hypothesis test?** The P-value is \( \) the significance level of \( \alpha = 0.01 \), so \( \) the null hypothesis. There \( \) evidence to warrant rejection of the claim that women and men have equal success in challenging calls. **b. Test the claim by constructing an appropriate confidence interval:** The 99% confidence interval is \( < (p_1 - p_2) < \) (Round to three decimal places as needed.)
**Understanding the Conclusion Based on a Confidence Interval**

**Question:**  
What is the conclusion based on the confidence interval?

**Explanation:**  
The confidence interval is a range of values used to estimate the true value of a parameter. Interpreting it helps determine if there is a significant difference between two groups—in this case, the success of men and women in challenging calls.

**Sentence Analysis:**  
"Because the confidence interval limits [Blank 1] 0, there [Blank 2] appear to be a significant difference between the two proportions. There [Blank 3] evidence to warrant rejection of the claim that men and women have equal success in challenging calls."

**Answer Choices:**

- **A.** The confidence interval suggests that there is a significant difference between the success of men and women in challenging calls. It is reasonable to speculate that women have more success.
  
- **B.** The confidence interval suggests that there is no significant difference between the success of men and women in challenging calls.
  
- **C.** The confidence interval suggests that there is a significant difference between the success of men and women in challenging calls. It is reasonable to speculate that men have more success.
  
- **D.** There is not enough information to reach a conclusion.

**Conclusion:**  
By analyzing the blanks in the sentence, the confidence interval's relationship to zero determines the presence of a significant difference. Selecting the appropriate terms to fill the blanks helps conclude whether the data suggests one gender has more success in challenging calls or if there is no significant difference at all.
Transcribed Image Text:**Understanding the Conclusion Based on a Confidence Interval** **Question:** What is the conclusion based on the confidence interval? **Explanation:** The confidence interval is a range of values used to estimate the true value of a parameter. Interpreting it helps determine if there is a significant difference between two groups—in this case, the success of men and women in challenging calls. **Sentence Analysis:** "Because the confidence interval limits [Blank 1] 0, there [Blank 2] appear to be a significant difference between the two proportions. There [Blank 3] evidence to warrant rejection of the claim that men and women have equal success in challenging calls." **Answer Choices:** - **A.** The confidence interval suggests that there is a significant difference between the success of men and women in challenging calls. It is reasonable to speculate that women have more success. - **B.** The confidence interval suggests that there is no significant difference between the success of men and women in challenging calls. - **C.** The confidence interval suggests that there is a significant difference between the success of men and women in challenging calls. It is reasonable to speculate that men have more success. - **D.** There is not enough information to reach a conclusion. **Conclusion:** By analyzing the blanks in the sentence, the confidence interval's relationship to zero determines the presence of a significant difference. Selecting the appropriate terms to fill the blanks helps conclude whether the data suggests one gender has more success in challenging calls or if there is no significant difference at all.
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