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.