Assume a significance level of a = 0.05 and use the given information to complete parts (a) and (b) below. Original claim: The standard deviation of pulse rates of a certain group of adult males is more than 19 bpm. The hypothesis test results in a P-value of 0.3695. a. State a conclusion about the null hypothesis. (Reject Ho or fail to reject Ho.) Choose the correct answer below. O A. Reject Ho because the P-value is greater than a. B. Fail to reject Ho because the P-value is greater than a. C. Fail to reject Ho because the P-value is less than or equal to a. D. Reject Ho because the P-value is less than or equal to a.

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### Hypothesis Testing: Significance Level and P-value Interpretation

Assume a significance level of α = 0.05 and use the given information to complete parts (a) and (b) below.

### Problem Scenario
**Original claim:** The standard deviation of pulse rates of a certain group of adult males is more than 19 bpm. The hypothesis test results in a P-value of 0.3695.

**a. State a conclusion about the null hypothesis.** (Reject H₀ or fail to reject H₀.) Choose the correct answer below.

#### Answer Choices:
- **A.** Reject H₀ because the P-value is greater than α.
- **B.** Fail to reject H₀ because the P-value is greater than α.
- **C.** Fail to reject H₀ because the P-value is less than or equal to α.
- **D.** Reject H₀ because the P-value is less than or equal to α.

#### Explanation:
To determine the conclusion about the null hypothesis (H₀), compare the P-value to the significance level (α):

- If the P-value is less than or equal to the significance level (α), we reject the null hypothesis (H₀).
- If the P-value is greater than the significance level (α), we fail to reject the null hypothesis (H₀).

Given that the P-value (0.3695) is greater than the significance level (α = 0.05), we fail to reject the null hypothesis.

Thus, the correct answer is:
- **B. Fail to reject H₀ because the P-value is greater than α.**
Transcribed Image Text:### Hypothesis Testing: Significance Level and P-value Interpretation Assume a significance level of α = 0.05 and use the given information to complete parts (a) and (b) below. ### Problem Scenario **Original claim:** The standard deviation of pulse rates of a certain group of adult males is more than 19 bpm. The hypothesis test results in a P-value of 0.3695. **a. State a conclusion about the null hypothesis.** (Reject H₀ or fail to reject H₀.) Choose the correct answer below. #### Answer Choices: - **A.** Reject H₀ because the P-value is greater than α. - **B.** Fail to reject H₀ because the P-value is greater than α. - **C.** Fail to reject H₀ because the P-value is less than or equal to α. - **D.** Reject H₀ because the P-value is less than or equal to α. #### Explanation: To determine the conclusion about the null hypothesis (H₀), compare the P-value to the significance level (α): - If the P-value is less than or equal to the significance level (α), we reject the null hypothesis (H₀). - If the P-value is greater than the significance level (α), we fail to reject the null hypothesis (H₀). Given that the P-value (0.3695) is greater than the significance level (α = 0.05), we fail to reject the null hypothesis. Thus, the correct answer is: - **B. Fail to reject H₀ because the P-value is greater than α.**
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