Question 18, 7.2.3 HW Score: $18.29 \%, 15$ of 82 points Part 1 of 3 Points: 0.33 of 1 The P-value for a hypothesis test is shown. Use the P-value to decide whether to reject $H_{0}$ when the level of significance is (a) $\alpha=0.01,(b) \alpha=0.05$, and (c) $\alpha=0.10$. \[ P=0.0609 \] (a) Do you reject or fail to reject $\mathrm{H}_{0}$ at the 0.01 level of significance? A. Fail to reject $\mathrm{H}_{0}$ because the P-value, 0.0609 , is less than $\alpha=0.01$. B. Reject $\mathrm{H}_{0}$ because the P-value, 0.0609 , is greater than $\alpha=0.01$. C. Reject $\mathrm{H}_{0}$ because the $\mathrm{P}$-value, 0.0609 , is less than $\alpha=0.01$. D. Fail to reject $\mathrm{H}_{0}$ because the P-value, 0.0609 , is greater than $\alpha=0.01$.
Solution
Step 1 ：Given that the P-value is 0.0609 and the level of significance (α) is 0.01.
Step 2 ：The P-value is a measure of the probability that an observed difference could have occurred just by random chance. The lower the P-value, the greater the statistical significance of the observed difference.
Step 3 ：If the P-value is less than or equal to the level of significance (α), we reject the null hypothesis. If the P-value is greater than α, we fail to reject the null hypothesis.
Step 4 ：In this case, the P-value is 0.0609 and the level of significance is 0.01. We need to compare these two values to decide whether to reject or fail to reject the null hypothesis.
Step 5 ：Since the P-value (0.0609) is greater than the level of significance (0.01), we fail to reject the null hypothesis.
Step 6 ：\(\boxed{\text{Final Answer: Fail to reject } H_{0} \text{ because the P-value, 0.0609, is greater than } \alpha=0.01.}\)
