One personality test available on the World Wide Web as a step section designed to assess the honesty of the test taker you are interested in the mean score among the general population on this subsection. The website reports that you is 140 but you have a good reason to believe that you differs from 140 you decide to do a statistical test you choose a random sample of people and have them take the personality test, you find that that means score on the sub section is 146 and a standard deviation of the scores is 25. what are the null hypothesis H0 and the alternative hypothesis H1 one that should be used for the test suppose that you decide not to recheck the hypothesis what sort of error might you be making?

In this scenario, you're conducting a hypothesis test to determine whether the mean score of the honesty subsection on a personality test differs from the reported value of 140. Let's break this down:

### **1. Setting Up the Hypotheses**

- **Null Hypothesis (\(H_0\))**: The null hypothesis states that the mean score of the honesty subsection among the general population is equal to the reported value.
  \[
  H_0: \mu = 140
  \]

- **Alternative Hypothesis (\(H_1\))**: The alternative hypothesis states that the mean score of the honesty subsection among the general population is different from the reported value (it could be either higher or lower).
  \[
  H_1: \mu \neq 140
  \]

This is a two-tailed test because you are testing whether the mean differs from 140 in either direction.

### **2. Type of Error**

When performing a hypothesis test, two types of errors can occur:

- **Type I Error**: This occurs when you reject the null hypothesis (\(H_0\)) when it is actually true. In your case, this would mean concluding that the mean score differs from 140 when, in reality, it does not.
  
- **Type II Error**: This occurs when you fail to reject the null hypothesis (\(H_0\)) when it is actually false. In your case, this would mean concluding that the mean score is 140 when, in reality, it is different.

### **What Error Might You Be Making?**

If you decide **not to reject the null hypothesis** after conducting the test, you might be making a **Type II Error**. This means that even though the sample mean is 146, you might incorrectly conclude that the population mean is still 140 when it is actually different.

Would you like more details on this process or any further clarification?

---

**Relative Questions:**

1. What are the consequences of making a Type I error in this scenario?
2. How can you determine the significance level (\(\alpha\)) for your hypothesis test?
3. What sample size is needed to increase the power of the test?
4. How does the standard deviation affect the hypothesis test?
5. What is the p-value, and how is it used in hypothesis testing?
6. How would you interpret a confidence interval for the mean score?
7. How can you control the risk of making a Type II error?
8. What are the assumptions underlying the hypothesis test you've chosen?

**Tip:** Remember, the choice of significance level (\(\alpha\)) directly influences the likelihood of making a Type I error. Common choices are 0.05 or 0.01, but the context of the study can guide this decision.

Explore the process of hypothesis testing to determine if the mean score of a personality test subsection differs from the reported value of 140. Learn about Type I and Type II errors in statistical inference with a practical example. Ideal for advanced undergraduate students and researchers.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation