- T-test for two related samples - Statistics problem -

A teacher believes that students who work more than 20 hours per week at a job will do worse on her tests than students who work fewer than 20 hours per week at a job. The teacher learned that the 26 students in her class all worked more than 20 hours per week. To test her hypothesis, the teacher got grant money for the students in her class so all 26 students could afford reduce their hours at work to below 20 hours. She gave the students two tests-- one test when they were all working more than 20 hours, and a second test after they had all reduced their work hours to less than 20. The correlation between the students' scores on the first test and the second test was r = +.75.

The following is a summary of the grades for these students on the first test, i.e., before they reduced their hours at work to less 20 hours:

M₁=75

s₁=5.3 (this is the unbiased sample standard deviation)

The following is a summary of the grades for these students on the second test, i.e., after they reduced their hours at work to less than 20 hours:

M₂=80

s₂=5.5 (this is the unbiased sample standard deviation)

Perform a t-test between two related samples by answering the questions below. Use an alpha-level of =.01.

0. Is this a one-tailed test or a two-tailed test?

1. What is the research hypothesis, H₁?

2. What is the null hypothesis, H₀?

3. What is the degrees of freedom for this problem, df?

4. What is the critical value of t, t_crit? (Be sure to use a + or a - sign for your answer.)

5. What is the mean of the distribution of the difference between correlated sample means, _M1-M2?

6. What is the standard deviation of the distribution of the difference between correlated sample means, _diff?

7. What is the t-score of the difference between sample means, M₁-M₂?

8. Based on the relation between the critical value of t and the t-score of the difference between sample means, can you reject the null hypothesis?

9. Based on whether or not you can reject the null hypothesis, can you accept the research hypothesis?

10. Find the 95% confidence interval for ₁-₂.

11. Find the 99% confidence interval for ₁-₂.

Show your work for all problems.

Thank you.