Create a 90% confidence interval for the true average cholesterol level of the general US male population.11. What is the 90% confidence interval?12. What is the correct interpretation of the confidence interval from question 11?13. Are the assumptions met? Explain. Conduct a hypothesis test at the 0.10 significance level to test the researcher’s question.14. What are the hypotheses?15. What is the significance level? A. 0.01 B. 0.04 C. 0.05 D. 0.1016. What is the value of the test statistic?17. What is the p-value?18. What is the correct decision? A. Reject the Null Hypothesis B. Fail to Reject the Null Hypothesis C. Accept the Null Hypothesis D. Accept the Alternative Hypothesis19. What is the appropriate conclusion/interpretation?20. Are the assumptions met? Explain. ### Statistical Analysis of Cholesterol Levels**Use the following information for questions 11-20:**The average cholesterol level in the general US population is 189 mg/dL. A researcher wants to see if the average cholesterol for men in the US is different from 189 mg/dL. She takes a sample of 81 American males and finds a sample mean of 194 mg/dL and a sample standard deviation of 10.4.For example, if you are asked to conduct a hypothesis test to determine whether the mean cholesterol level for men differs from the general population mean of 189 mg/dL, you would compare the sample mean (194 mg/dL) to the population mean (189 mg/dL) using statistical methods such as a t-test or z-test.- **Population mean (μ):** 189 mg/dL- **Sample size (n):** 81- **Sample mean (x̄):** 194 mg/dL- **Sample standard deviation (s):** 10.4**Steps you might follow for a hypothesis test:**1. **Formulate Hypotheses:** - Null hypothesis (H0): The mean cholesterol level for men is equal to 189 mg/dL (H0: μ = 189). - Alternative hypothesis (H1): The mean cholesterol level for men is not equal to 189 mg/dL (H1: μ ≠ 189).2. **Calculate the Test Statistic:** - Use the given sample mean, population mean, sample standard deviation, and sample size to calculate the test statistic.3. **Determine the P-value or Critical Value:** - Compare the test statistic to critical values from the t-distribution (or z-distribution, as appropriate) to determine whether to reject the null hypothesis.4. **Interpret the Results:** - Based on the comparison of the test statistic and critical values (or P-value), conclude whether there is sufficient evidence to reject the null hypothesis and determine if the average cholesterol level for men is different from 189 mg/dL.

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Create a 90% confidence interval for the true average cholesterol level of the general US male population.

11. What is the 90% confidence interval?

12. What is the correct interpretation of the confidence interval from question 11?

13. Are the assumptions met? Explain. Conduct a hypothesis test at the 0.10 significance level to test the researcher’s question.

14. What are the hypotheses?

15. What is the significance level? A. 0.01 B. 0.04 C. 0.05 D. 0.10

16. What is the value of the test statistic?

17. What is the p-value?

18. What is the correct decision? A. Reject the Null Hypothesis B. Fail to Reject the Null Hypothesis C. Accept the Null Hypothesis D. Accept the Alternative Hypothesis

19. What is the appropriate conclusion/interpretation?

20. Are the assumptions met? Explain.

### Statistical Analysis of Cholesterol Levels

**Use the following information for questions 11-20:**

The average cholesterol level in the general US population is 189 mg/dL. A researcher wants to see if the average cholesterol for men in the US is different from 189 mg/dL. She takes a sample of 81 American males and finds a sample mean of 194 mg/dL and a sample standard deviation of 10.4.

For example, if you are asked to conduct a hypothesis test to determine whether the mean cholesterol level for men differs from the general population mean of 189 mg/dL, you would compare the sample mean (194 mg/dL) to the population mean (189 mg/dL) using statistical methods such as a t-test or z-test.

- **Population mean (μ):** 189 mg/dL
- **Sample size (n):** 81
- **Sample mean (x̄):** 194 mg/dL
- **Sample standard deviation (s):** 10.4

**Steps you might follow for a hypothesis test:**

1. **Formulate Hypotheses:**
- Null hypothesis (H0): The mean cholesterol level for men is equal to 189 mg/dL (H0: μ = 189).
- Alternative hypothesis (H1): The mean cholesterol level for men is not equal to 189 mg/dL (H1: μ ≠ 189).

2. **Calculate the Test Statistic:**
- Use the given sample mean, population mean, sample standard deviation, and sample size to calculate the test statistic.

3. **Determine the P-value or Critical Value:**
- Compare the test statistic to critical values from the t-distribution (or z-distribution, as appropriate) to determine whether to reject the null hypothesis.

4. **Interpret the Results:**
- Based on the comparison of the test statistic and critical values (or P-value), conclude whether there is sufficient evidence to reject the null hypothesis and determine if the average cholesterol level for men is different from 189 mg/dL.

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