(c)Suppose the true mean hourly wage for foodservice workers in the U.S. this year is $8.08. Fill in the blanks to describe a Type I error. A type I error would be rejecting/failing to reject the hypothesis that  is blank blank, when in fact u is equal to 

### Describing a Type I Error

Let's fill in the blanks to describe a Type I error, given the scenario.

**Hypotheses:**
- Null Hypothesis ($ H_0 $): $\mu \leq 8.08$
- Alternative Hypothesis ($ H_1 $): $\mu > 8.08$

**True Mean Wage:**
- True mean hourly wage ($\mu$) = $8.08

**Type I Error Description:**

A Type I error would be **rejecting** the hypothesis that $\mu$ is **less than or equal to $8.08**, when in fact $\mu$ is equal to $8.08.

So, the filled-in description is:

**A Type I error would be rejecting the hypothesis that $\mu$ is less than or equal to $8.08, when in fact $\mu$ is equal to $8.08.**

### Related Questions

1. What is the probability of making a Type I error called?
2. How is the significance level ($\alpha$) chosen in hypothesis testing?
3. What are the consequences of making a Type I error in this context?
4. How can one reduce the likelihood of committing a Type I error?
5. What role does the sample size play in hypothesis testing?
6. How do you interpret a p-value in the context of Type I error?
7. What is the difference between Type I and Type II errors?
8. How does the choice of a one-tailed test affect the probability of making a Type I error?

#### Tip
When designing a hypothesis test, it is essential to balance the risks of Type I and Type II errors by choosing an appropriate significance level and ensuring a sufficiently large sample size.

Explore the concept of Type I error in hypothesis testing through a detailed example. Learn how to identify and describe Type I errors, using the scenario of foodservice workers' hourly wages in the U.S. Understand the significance level and implications of rejecting the null hypothesis incorrectly. Suitable for advanced high school and college students studying statistics and hypothesis testing.

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