In each part, we have given the significance level and the P-value for a hypothesis test. For each case determine if the null hypothesis should be rejected. Write "reject" or "do not reject" (without quotations). Double check that you have typed your answers correctly (no spelling errors) BEFORE you submit. In order to allow you more than one attempt at this problem, the problem will not tell you which part(s) are correct if you do not get all parts correct.

(a)  α=0.06,P=0.06α=0.06,P=0.06
answer:

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(b)  α=0.07,P=0.06α=0.07,P=0.06
answer:

(c)  α=0.01,P=0.06α=0.01,P=0.06
answer

For hypothesis testing, the decision rule is based on comparing the P-value to the significance level \( \alpha \):

- If \( P \leq \alpha \), **reject** the null hypothesis.
- If \( P > \alpha \), **do not reject** the null hypothesis.

Now, let's apply this to each part:

**(a)** \( \alpha = 0.06, P = 0.06 \)
- Since \( P = \alpha \), we reject the null hypothesis.
- **Answer:** reject

**(b)** \( \alpha = 0.07, P = 0.06 \)
- Since \( P < \alpha \), we reject the null hypothesis.
- **Answer:** reject

**(c)** \( \alpha = 0.01, P = 0.06 \)
- Since \( P > \alpha \), we do not reject the null hypothesis.
- **Answer:** do not reject

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Would you like any further clarification on this problem or its concepts?

**Relative Questions:**
1. What is the interpretation of a P-value in hypothesis testing?
2. How is the significance level \( \alpha \) chosen in practice?
3. What happens when \( P = \alpha \) in a hypothesis test?
4. Can you explain the consequences of rejecting the null hypothesis when it is actually true?
5. How does increasing \( \alpha \) affect the likelihood of rejecting the null hypothesis?

**Tip:** The significance level \( \alpha \) is a threshold for how much risk of a Type I error (false positive) you are willing to accept when rejecting the null hypothesis.

In each part, we have given the significance level and the P-value for a hypothesis test. For each case determine if the null hypothesis should be rejected. Write 'reject' or 'do not reject' (without quotations). Double check that you have typed your answers correctly (no spelling errors) BEFORE you submit. In order to allow you more than one attempt at this problem, the problem will not tell you which part(s) are correct if you do not get all parts correct.

(a) α=0.06, P=0.06
(b) α=0.07, P=0.06
(c) α=0.01, P=0.06

Learn how to determine whether to reject or not reject a null hypothesis based on significance level and P-value. This problem provides a step-by-step approach to hypothesis testing with examples for different α and P values, highlighting key statistical concepts in decision-making.

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