An anger-management course claims that, after completing its seminar, participants will lose their tempers less often. Always a skeptic, you decide to test this claim. A random sample of 12
 seminar participants is chosen, and these participants are asked to record the number of times that they lost their tempers in the two weeks prior to the course. After the course is over, the same participants are asked to record the number of times that they lost their tempers in the next two weeks. The following table lists the results of the survey. Using these data, test the claim at the 0.02
 level of significance assuming that the population distribution of the paired differences is approximately normal. Let d=
 (participants after completing the anger-management course) −
(participants before completing the anger-management course). 

To test the claim that participants lose their tempers less often after completing the anger-management course, we can conduct a **paired-sample t-test**. This test is appropriate since we have paired data (before and after the seminar for each participant) and we are interested in the difference in the number of temper incidents.

The null hypothesis (\( H_0 \)) and the alternative hypothesis (\( H_a \)) for this test are:

- \( H_0: \mu_d = 0 \) (there is no difference in the number of temper incidents before and after the course, i.e., the course had no effect).
- \( H_a: \mu_d > 0 \) (the number of temper incidents after the course is less than before, meaning \( d \) (after - before) is negative, indicating the course had a positive effect).

### Steps to Perform the Paired-Sample t-Test:

1. **Calculate the differences**: For each participant, calculate the difference in the number of temper incidents: \( d_i = \text{after} - \text{before} \).

2. **Calculate the mean of the differences**: \( \bar{d} = \frac{\sum d_i}{n} \).

3. **Calculate the standard deviation of the differences**: Use the formula:
   \[
   s_d = \sqrt{\frac{\sum (d_i - \bar{d})^2}{n - 1}}
   \]
   
4. **Calculate the test statistic**: The test statistic for the paired t-test is given by:
   \[
   t = \frac{\bar{d}}{s_d / \sqrt{n}}
   \]
   where \( n \) is the number of participants (in this case, \( n = 12 \)).

5. **Determine the critical value**: Use the t-distribution table to find the critical value for \( \alpha = 0.02 \) and \( df = n - 1 = 11 \).

6. **Compare the test statistic with the critical value**: If the test statistic is greater than the critical value, reject the null hypothesis.

---

### To proceed, I need the data (the number of temper incidents before and after the course for each of the 12 participants). Could you provide that information, or should I make up an example to show how to calculate it?



An anger-management course claims that, after completing its seminar, participants will lose their tempers less often. Always a skeptic, you decide to test this claim. A random sample of 12 seminar participants is chosen, and these participants are asked to record the number of times that they lost their tempers in the two weeks prior to the course. After the course is over, the same participants are asked to record the number of times that they lost their tempers in the next two weeks. The following table lists the results of the survey. Using these data, test the claim at the 0.02 level of significance assuming that the population distribution of the paired differences is approximately normal. Let d= (participants after completing the anger-management course) − (participants before completing the anger-management course).

Test the effectiveness of an anger-management course using a paired-sample t-test at a 0.02 significance level. Learn how to calculate the mean of differences, standard deviation, and test statistic. Suitable for students in advanced high school or undergraduate statistics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation