A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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**Educational Content on Hypothesis Testing**

**Problem Statement:**
Consider a sample of 52 football games, where 31 of them were won by the home team. Use a 0.10 significance level to test the claim that the probability that the home team wins is greater than one-half.

**Identify the Null and Alternative Hypotheses:**
Choose the correct answer below.

- A. \( H_0: p > 0.5 \)  
  \( H_1: p = 0.5 \)

- B. \( H_0: p = 0.5 \)  
  \( H_1: p \neq 0.5 \)

- C. \( H_0: p = 0.5 \)  
  \( H_1: p > 0.5 \)

- D. \( H_0: p = 0.5 \)  
  \( H_1: p < 0.5 \)

**Answer:**
C. \( H_0: p = 0.5 \)  
\( H_1: p > 0.5 \)

**Identify the Test Statistic for this Hypothesis Test:**

The test statistic for this hypothesis test is ____.  
*(Round to two decimal places as needed.)*

**Identify the P-value for this Hypothesis Test:**

The P-value for this hypothesis test is ____.  
*(Round to three decimal places as needed.)*

**Identify the Conclusion for this Hypothesis Test:**

- A. Reject \( H_0 \). There is sufficient evidence to support the claim that the probability of the home team winning is greater than one-half.

- B. Fail to reject \( H_0 \). There is sufficient evidence to support the claim that the probability of the home team winning is greater than one-half.

- C. Reject \( H_0 \). There is not sufficient evidence to support the claim that the probability of the home team winning is greater than one-half.

- D. Fail to reject \( H_0 \). There is not sufficient evidence to support the claim that the probability of the home team winning is greater than one-half.

**Answer:**
D. Fail to reject \( H_0 \). There is not sufficient evidence to support the claim that the probability of the home team winning is greater than one-half.
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Transcribed Image Text:**Educational Content on Hypothesis Testing** **Problem Statement:** Consider a sample of 52 football games, where 31 of them were won by the home team. Use a 0.10 significance level to test the claim that the probability that the home team wins is greater than one-half. **Identify the Null and Alternative Hypotheses:** Choose the correct answer below. - A. \( H_0: p > 0.5 \) \( H_1: p = 0.5 \) - B. \( H_0: p = 0.5 \) \( H_1: p \neq 0.5 \) - C. \( H_0: p = 0.5 \) \( H_1: p > 0.5 \) - D. \( H_0: p = 0.5 \) \( H_1: p < 0.5 \) **Answer:** C. \( H_0: p = 0.5 \) \( H_1: p > 0.5 \) **Identify the Test Statistic for this Hypothesis Test:** The test statistic for this hypothesis test is ____. *(Round to two decimal places as needed.)* **Identify the P-value for this Hypothesis Test:** The P-value for this hypothesis test is ____. *(Round to three decimal places as needed.)* **Identify the Conclusion for this Hypothesis Test:** - A. Reject \( H_0 \). There is sufficient evidence to support the claim that the probability of the home team winning is greater than one-half. - B. Fail to reject \( H_0 \). There is sufficient evidence to support the claim that the probability of the home team winning is greater than one-half. - C. Reject \( H_0 \). There is not sufficient evidence to support the claim that the probability of the home team winning is greater than one-half. - D. Fail to reject \( H_0 \). There is not sufficient evidence to support the claim that the probability of the home team winning is greater than one-half. **Answer:** D. Fail to reject \( H_0 \). There is not sufficient evidence to support the claim that the probability of the home team winning is greater than one-half.
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