1. Stat 350 Lab Session GSI: Yizao Wang Section 016 Mon 2pm30-4pm MH 444-D Section 043 Wed 2pm30-4pm MH 444-B

2. Outline Module 8, Two-Independent Samples t Test P-value Practice Midterm Feedback Please login with your UMID today.

3. Two-Independent Samples t Test Used when comparing the means of two populations that are not related or matched in any way Null hypothesis: μ1 – μ2 = 0 Assumptions: (a) Each sample is a random sample from each of the two populations. (b) Two random samples are independent of each other. (c) Each population is (approximately) a normal population. (d) For the pooled version we additionally assume that the populations have equal population variance (standard deviation). General and pooled versions have different test statistic formulas.

4. Two-Independent Samples t Test Determining general vs. pooled (p 51) Compare sample standard deviations similar s1 and s2 => pooled Compare IQRs (by boxplots) similar lengths => pooled Levene’s test p-value > α = 0.05 => pooled

5. Module 8 Activity Background: A total of 38 college freshmen were administered the Survey of Study Habits and Attitudes (SSHA), a psychological test designed to measure motivation and attitude towards study habits in college students, at a private college. The 38 students were a simple random sample, of which 18 were female and 20 were male. Ctools SSHA.sav Task: Perform a two-independent samples t-test to assess if there is a difference between the mean score for women on the test and the mean score for men on the test. Page 50-54

6. What is the specific parameter of interest? p μ μ d μ 1 – μ 2 p 1 – p 2

7. Select the appropriate alternative hypothesis Ha: μ ≠ 0 Ha: μ d ≠ 0 Ha: μ 1 – μ 2 ≠ 0

8. Select the appropriate assumptions for this test. Choose all that apply... A)Random sample B)Normal population C)Independent samples

9. A and B are wrong! Why? A)Random sample. B)Normal population. A)Both samples (the observed 20 male and 18 female SSHA scores) are random. B)Both populations (all male and all female SSHA scores) follow a normal distribution.

10. How many QQ-plots are needed to check the normality assumption? 2 1 0 – you should use a sequence plot

11. What is the value of the test statistic? A)2.032 B)2.056

12. What is the distribution of the test statistics if Ho is true? A)N(0,1) B)N(μ,σ) C)t(n-1) D)t(min{n 1 -1, n 2 -1}) E)t(n 1 +n 2 -2)

13. What is the p-value? A)0.05 B)0.05/2 C)0.047 D)0.047/2

14. Yes or No Are the results statistically significant at the 5% level?

15. Yes or No Based on the 95% confidence interval of (0.042, 39.569), would you reject H o at the 5% level?

16. Module 8 Good summary on three t test scenarios p57 One sample t test Paired t test Two-independent samples t test Exercise on t test scenarios p58

17. P-Value Practice State the p-value expression p-value = P (t direction value) Sketch the t-distribution and shadow the desired tail (tails) Find the bounds of (interval including) p-value Decision

18. Midterm Feedback Please finish the anonymous survey at the following link: http://www.surveymonkey.com/s.aspx?sm =z0UmqIhkg4NY92fmlZds6g_3d_3d http://www.surveymonkey.com/s.aspx?sm =z0UmqIhkg4NY92fmlZds6g_3d_3d The link is emailed to your mailbox@umich. Any comments on Yizao’s teaching will be warmly welcomed.

19. Extra Credit Opportunity Exam 2 is only 3 weeks away! There will be another extra credit opportunity next week (March 17 to 21) –Two points added to your 2 nd midterm score Mark your calendars now - the link will be on Ctools soon. Have you got your extra credit for first midterm? Check it on Ctools.