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.