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The image shows a statistics problem related to hypothesis testing. Here's a breakdown of the problem and how to answer it.

### Problem:
- **Significance level (α)**: 0.05
- **Original claim**: The mean pulse rate of a group of adult males is 74 bpm.
- **P-value**: 0.0075

The question asks you to determine the appropriate conclusion about the null hypothesis (H₀) and make a final conclusion in non-technical terms.

#### Part (a) asks for a conclusion regarding the null hypothesis (H₀):
- **H₀**: The mean pulse rate of the group of adult males is 74 bpm.
- The **P-value** is 0.0075, which is **less than** the significance level (α = 0.05).
  
According to hypothesis testing principles:
- If the **P-value ≤ α**, we **reject H₀**.
- If the **P-value > α**, we **fail to reject H₀**.

In this case, since 0.0075 < 0.05, we **reject the null hypothesis (H₀)**.

The correct answer for part (a) is:
- **D. Reject H₀ because the P-value is less than or equal to α.**

#### Part (b) asks for a final conclusion in non-technical terms:
Since we rejected the null hypothesis, the original claim that the mean pulse rate is 74 bpm is not supported by the data. There is enough evidence to conclude that the mean pulse rate is **not** 74 bpm.

The correct answer for part (b) is:
- **B. There is sufficient evidence to warrant rejection of the claim that the mean pulse rate (in beats per minute) of the group of adult males is 74 bpm.**

### Would you like any further explanation on hypothesis testing or P-values?

Here are 5 related questions to deepen your understanding:
1. What is the role of the significance level (α) in hypothesis testing?
2. How do you interpret a P-value in the context of hypothesis testing?
3. What are Type I and Type II errors in hypothesis testing?
4. How would the conclusion change if the P-value were greater than 0.05?
5. Why is it important to state conclusions both in technical and non-technical terms?

**Tip**: Always compare the P-value to the significance level to determine whether to reject or fail to reject the null hypothesis.

Assume a significance level of α = 0.05 and use the given information to complete parts (a) and (b). The original claim is that the mean pulse rate of a group of adult males is 74 bpm. The hypothesis test results in a P-value of 0.0075. What is the correct conclusion about the null hypothesis?

Learn how to interpret a hypothesis test where the original claim is that the mean pulse rate of a group of adult males is 74 bpm. Given a significance level of 0.05 and a P-value of 0.0075, this problem demonstrates how to reject the null hypothesis.

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