Question 1 A local pizza restaurant has started delivery service. The owner claims that the mean delivery time is less than 30 minutes. In a hypothesis test of this claim, sample data was collected resulting in a p-value equal to 0.0746 . Which of the following significance levels leads to the decision "Reject $\mathrm{H}_{0}$ "? I. $a=1 \%$ II. $a=5 \%$ III. $a=10 \%$ I only
Solution
Step 1 ：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 2 ：In hypothesis testing, if the p-value is less than or equal to the significance level (\(\alpha\)), we reject the null hypothesis.
Step 3 ：Given that the p-value is 0.0746, we compare this value with the significance levels provided:
Step 4 ：For \(\alpha = 1\% = 0.01\), since 0.0746 > 0.01, we do not reject the null hypothesis at this significance level.
Step 5 ：For \(\alpha = 5\% = 0.05\), since 0.0746 > 0.05, we do not reject the null hypothesis at this significance level.
Step 6 ：For \(\alpha = 10\% = 0.10\), since 0.0746 < 0.10, we reject the null hypothesis at this significance level.
Step 7 ：Therefore, the significance level that leads to the decision "Reject H0" is \(\alpha = 10\%\).
Step 8 ：\(\boxed{\text{The significance level that leads to the decision "Reject H0" is } \alpha = 10\%}\)
