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Stat 350 Lab Session GSI: Yizao Wang Section 016 Mon 2pm30-4pm MH 444-D Section 043 Wed 2pm30-4pm MH 444-B. Outline. Module 8, Two-Independent Samples t Test P-value Practice Midterm Feedback Please login with your UMID today. Two-Independent Samples t Test.

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Outline

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  1. Stat 350 Lab SessionGSI: Yizao WangSection 016 Mon 2pm30-4pm MH 444-DSection 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) Eachsample is a random sample from each of the two populations.(b) Two random samples are independent of each other.(c) Eachpopulation is (approximately) a normal population.(d) For the pooled version we additionally assume that the populations have equalpopulation 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 deviationssimilar s1 and s2 => pooled • Compare IQRs (by boxplots)similar lengths => pooled • Levene’s testp-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 μd μ1 – μ2 p1 – p2

  7. Select the appropriate alternative hypothesis Ha: μ ≠ 0 Ha: μd ≠ 0 Ha: μ1 – μ2 ≠ 0

  8. Select the appropriate assumptions for this test. Choose all that apply... • Random sample • Normal population • Independent samples

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

  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? • 2.032 • 2.056

  12. What is the distribution of the test statistics if Ho is true? • N(0,1) • N(μ,σ) • t(n-1) • t(min{n1-1, n2-1}) • t(n1+n2-2)

  13. What is the p-value? • 0.05 • 0.05/2 • 0.047 • 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 Ho at the 5% level?

  16. Module 8 • Good summary on three t test scenarios p57One sample t testPaired t testTwo-independent samples t test • Exercise on t test scenarios p58

  17. P-Value Practice • State the p-value expressionp-value = P (t directionvalue) • 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 • 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 2nd 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.

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