Last year's mean hourly wage (in dollars) for all hospital clerical workers in a large state was 8.25. An administrator for the state believes that this year's mean hourly wage for hospital clerical workers is greater than last year's mean. She hires statisticians to sample a number of hospital clerical workers and to carry out a hypothesis test. State the null hypothesis H0 and the alternative hypothesis H1 that would be used for this test.

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.

Explore the concepts of null and alternative hypotheses in hypothesis testing. Learn how to set up hypotheses for testing whether this year's mean hourly wage for hospital clerical workers is greater than last year's. Suitable for advanced statistical analysis.

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