e) We are performing a hypothesis test where $\mathrm{H}_{1}: \mu> 50$. If the test is done at the $5 \%$ significance level and the truth is that $\mu=17$, then what percentage of the time should we expect to Reject the null hypothesis in the long run?
$0 \%$
$1 \%$
$5 \%$
$10 \%$
$100 \%$

Step 1 ：The null hypothesis in this case is that \(\mu \leq 50\). We are given that the true value of \(\mu\) is 17, which is less than 50. Therefore, if we are performing the test correctly, we should not be rejecting the null hypothesis, because the true value of \(\mu\) is in fact consistent with the null hypothesis.

Step 2 ：In the long run, the percentage of the time that we should expect to reject the null hypothesis when it is true is equal to the significance level of the test. In this case, the significance level is 5%. However, since the true value of \(\mu\) is less than 50, we should not be rejecting the null hypothesis at all.

Step 3 ：Therefore, the percentage of the time that we should expect to reject the null hypothesis in the long run is 0%.

Step 4 ：Final Answer: The percentage of the time that we should expect to reject the null hypothesis in the long run is \(\boxed{0\%}\).