Assume a significance level of $$ \alpha=0.01 $$ 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 12 bpm. The hypothesis test results in a P-value of 0.3434 . C. Fail to reject $$ H_{0} $$ because the P-value is less than or equal to $$ \alpha $$. Fail to reject $$ H_{0} $$ because the P-value is greater than $$ \alpha $$. D. Reject $$ H_{0} $$ because the P-value is greater than $$ \alpha $$. b. Without using technical terms, state a final conclusion that addresses the original claim. Which of the following is the correct conclusion? A. The standard deviation of pulse rates of the group of adult males is more than 12 bpm. B. There is not sufficient evidence to support the claim that the standard deviation of pulse rates of the group of adult males is more than 12 bpm. C. The standard deviation of pulse rates of the group of adult males is less than or equal to 12 bpm. D. There is sufficient evidence to support the claim that the standard deviation of pulse rates of the group of adult males is more than 12 bpm.

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UpStudy AI · Accepted Answer

To solve the problem, we need to analyze the hypothesis test results based on the given significance level and P-value.

### Step 1: Extract Known Conditions
- **Significance Level ($$ \alpha $$)**: 0.01
- **P-value**: 0.3434
- **Original Claim**: The standard deviation of pulse rates of a certain group of adult males is more than 12 bpm.

### Step 2: Analyze the Hypothesis Test
1. **Null Hypothesis ($$ H_0 $$)**: The standard deviation of pulse rates is less than or equal to 12 bpm.
2. **Alternative Hypothesis ($$ H_1 $$)**: The standard deviation of pulse rates is more than 12 bpm.

### Step 3: Decision Rule
- If the P-value is less than or equal to $$ \alpha $$, we reject $$ H_0 $$.
- If the P-value is greater than $$ \alpha $$, we fail to reject $$ H_0 $$.

### Step 4: Compare P-value with $$ \alpha $$
- Given P-value: 0.3434
- Significance Level: 0.01

Since $$ 0.3434 > 0.01 $$, we **fail to reject $$ H_0 $$**.

### Step 5: Conclusion for Part (a)
The correct statement regarding the hypothesis test is:
- **C. Fail to reject $$ H_{0} $$ because the P-value is greater than $$ \alpha $$.**

### Step 6: Final Conclusion for Part (b)
Now, we need to state a final conclusion that addresses the original claim:
- Since we failed to reject $$ H_0 $$, we do not have sufficient evidence to support the claim that the standard deviation of pulse rates is more than 12 bpm.

The correct conclusion is:
- **B. There is not sufficient evidence to support the claim that the standard deviation of pulse rates of the group of adult males is more than 12 bpm.**

### Summary of Answers
- Part (a): C. Fail to reject $$ H_{0} $$ because the P-value is greater than $$ \alpha $$.
- Part (b): B. There is not sufficient evidence to support the claim that the standard deviation of pulse rates of the group of adult males is more than 12 bpm.
- **Part (a):** Fail to reject $$ H_{0} $$ because the P-value is greater than $$ \alpha $$. - **Part (b):** There is not sufficient evidence to support the claim that the standard deviation of pulse rates is more than 12 bpm.

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