You are conducting a study to see if the proportion of men over 50 who regularly have their prostate examined is significantly less than 0.47. You use a significance level of a = 0.005. Họ:p = 0.47 H1:p < 0.47 You obtain a sample of size 739 in which there are 322 successes. What is the test statistic for this sample? (Report answer accurate to 3 decimal places.) What is the p-value for this sample? (Report answer accurate to 4 decimal places.) This test statistic leads to a decision to O reject the null O accept the null O fail to reject the null As such, the final conclusion is that O there is sufficient evidence to conclude that the proportion of men over 50 who regularly have their prostate examined is less than 0.47. O there is not sufficient evidence to conclude that the proportion of men over 50 who regularly have their prostate examined is less than 0.47. O there is sufficient evidence to conclude that the proportion of men over 50 who regularly have their prostate examined is equal to 0.47. O there is not sufficient evidence to conclude that the proportion of men over 50 who regularly have their prostate examined is egual to 0,47.

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**Hypothesis Testing: Proportion of Men Over 50 Undergoing Prostate Exams**

In this study, you aim to determine if the proportion of men over 50 who regularly undergo prostate exams is significantly less than 0.47, using a significance level (α) of 0.005.

**Hypotheses:**

- Null Hypothesis (H₀): p = 0.47
- Alternative Hypothesis (H₁): p < 0.47

**Sample Data:**

- Sample size (n): 739
- Number of successes: 322

**Tasks:**

1. **Calculate the Test Statistic:**
   - Report your answer to three decimal places.

2. **Determine the p-value:**
   - Report your answer to four decimal places.

3. **Decision Making:**
   - Decide whether to reject, accept, or fail to reject the null hypothesis based on the test statistic.

**Conclusion Options:**

- There is sufficient evidence to conclude that the proportion of men over 50 who regularly have their prostate examined is less than 0.47.
- There is not sufficient evidence to conclude that the proportion of men over 50 who regularly have their prostate examined is less than 0.47.
- There is sufficient evidence to conclude that the proportion of men over 50 who regularly have their prostate examined is equal to 0.47.
- There is not sufficient evidence to conclude that the proportion of men over 50 who regularly have their prostate examined is equal to 0.47.

Remember to use the results from your calculations to make an informed decision regarding the final conclusion.

*Submit your answers to complete the question.*
Transcribed Image Text:**Hypothesis Testing: Proportion of Men Over 50 Undergoing Prostate Exams** In this study, you aim to determine if the proportion of men over 50 who regularly undergo prostate exams is significantly less than 0.47, using a significance level (α) of 0.005. **Hypotheses:** - Null Hypothesis (H₀): p = 0.47 - Alternative Hypothesis (H₁): p < 0.47 **Sample Data:** - Sample size (n): 739 - Number of successes: 322 **Tasks:** 1. **Calculate the Test Statistic:** - Report your answer to three decimal places. 2. **Determine the p-value:** - Report your answer to four decimal places. 3. **Decision Making:** - Decide whether to reject, accept, or fail to reject the null hypothesis based on the test statistic. **Conclusion Options:** - There is sufficient evidence to conclude that the proportion of men over 50 who regularly have their prostate examined is less than 0.47. - There is not sufficient evidence to conclude that the proportion of men over 50 who regularly have their prostate examined is less than 0.47. - There is sufficient evidence to conclude that the proportion of men over 50 who regularly have their prostate examined is equal to 0.47. - There is not sufficient evidence to conclude that the proportion of men over 50 who regularly have their prostate examined is equal to 0.47. Remember to use the results from your calculations to make an informed decision regarding the final conclusion. *Submit your answers to complete the question.*
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