To set up the hypotheses for this scenario, we need to define the null hypothesis ($H_0$) and the alternative hypothesis ($H_1$).

• The null hypothesis ($H_0$) represents the status quo or a statement of no effect or no difference. In this case, it suggests that this year's mean hourly wage for hospital clerical workers is not greater than last year's mean wage.

• The alternative hypothesis ($H_1$) is what the administrator is trying to support; it indicates that this year's mean hourly wage for hospital clerical workers is greater than last year's mean wage.

Thus, the hypotheses can be stated as:

• $H_0$: $\mu \leq 8.25$

• $H_1$: $\mu > 8.25$

Where $\mu$ represents the mean hourly wage for hospital clerical workers this year.

Do you want more details or have any questions?

Here are 8 related questions:

1. How do statisticians determine the sample size for hypothesis testing?
2. What is the significance level ($\alpha$) and how is it used in hypothesis testing?
3. How is the test statistic calculated for a hypothesis test?
4. What are Type I and Type II errors in the context of hypothesis testing?
5. How can confidence intervals be used alongside hypothesis testing?
6. What is the difference between a one-tailed and a two-tailed test?
7. How does the p-value relate to the null hypothesis?
8. What statistical tests are commonly used to test hypotheses about means?

Tip: Always check the assumptions of your statistical test before performing hypothesis testing to ensure the validity of your results.