For each pair of hypotheses that follows, decide whether H00 and H11 are set up correctly as the null and alternative hypotheses for a hypothesis test. If so, type “Valid” in the box. If not, type “Invalid” in the box.

**1**

H00: μ ≠ 230

H11: μ = 230

This setup is **Invalid**.

In hypothesis testing, the null hypothesis (\(H_0\)) typically states that there is no effect or no difference, while the alternative hypothesis (\(H_1\)) suggests that there is an effect or a difference.

Here, the null hypothesis \(H_0: \mu \neq 230\) indicates a difference, which is usually the role of the alternative hypothesis. The alternative hypothesis \(H_1: \mu = 230\) suggests equality, which is typically reserved for the null hypothesis.

The correct setup should be:
- \(H_0: \mu = 230\) (Null hypothesis — no difference)
- \(H_1: \mu \neq 230\) (Alternative hypothesis — difference exists)

Would you like more details on hypothesis testing or how to structure hypotheses? Here are 5 follow-up questions that may expand on the topic:

1. How do you determine the appropriate form of the null and alternative hypotheses?
2. What is the difference between a one-tailed and a two-tailed hypothesis test?
3. Can you explain the significance level (\(\alpha\)) in hypothesis testing?
4. How does a p-value relate to hypothesis testing?
5. What are Type I and Type II errors in hypothesis testing?

**Tip**: Always remember that the null hypothesis (\(H_0\)) usually represents the "status quo" or "no effect" assumption.

For each pair of hypotheses that follows, decide whether H00 and H11 are set up correctly as the null and alternative hypotheses for a hypothesis test. If so, type 'Valid' in the box. If not, type 'Invalid' in the box.

H00: μ ≠ 230
H11: μ = 230

Learn the correct setup of null (H₀) and alternative (H₁) hypotheses in hypothesis testing. In this example, H₀: μ ≠ 230 and H₁: μ = 230 is incorrect. Find out why and discover the proper format. This topic is key for college-level statistics courses.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation