- T-test for two independent 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. To test this belief, the teacher asked the 26 students in her class how many hours they work per week. She found that 13 students worked more than 20 hours per week, and 13 students worked fewer than 20 hours per week.

The following are the data from students who worked more than 20 hours per week:

n₁=13

M₁=75

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

The following are the data from students who worked fewer than 20 hours per week:

n₂=13

M₂=80

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

Perform a t-test 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 independent sample means, _M1-M2?

6. What is the standard deviation of the distribution of the difference between independent 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.