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3. Pooled CI for Difference in Population Means Pooled Two Independent-Samples t Confidence Interval for  1 -  2 where and and t* is the value from a t (n 1 + n 2 – 2) distribution. This interval requires we have independent random samples from normal populations with equal population variances. If the sample sizes are large (both > 30), the assumption of normality is not so crucial and the result is approximate.

4. Learning about the Difference in Two Popul Means Computer Package Notes: Most provide results for both unpooled and pooled two indep samples t procedures. Some provide Levene’s test for assessing if popul variances can be assumed equal.  Null hypothesis = population variances are equal.  Small p-value  reject null hypothesis and conclude pooled procedure should not be used. (10% level used, lab module 8.) Graphical tool for assessing equal population variance is side-by-side boxplots and comparing the IQRs. If lengths of boxes and ranges very different, pooled method may not be reasonable.

5. Learning about the Difference in Two Popul Means Pooled or Unpooled? Guidelines: If sample std devs similar, assumption of common population variance reasonable and pooled can be used. Note: pooled and unpooled standard errors equal anyway. Advantage for pooled version is df is simpler. But sample std devs almost never exactly equal. So how similar is similar enough? If larger std dev from group with larger sample size, pooled acceptable, conservative (produces wider interval). If smaller std dev from group with larger sample size, pooled produces misleading narrower interval. Bottom-line: Pool if reasonable; but if sample std devs not similar, we have unpooled.

6. Try It! Comparing Reading scores Study compared reading scores for students taught by certified teachers vs those taught by uncertified teachers  1 = average reading score for popul of students taught by certified teachers  2 = average reading score for popul of students taught by uncertified teachers

7. Try It! Comparing Reading scores (continued) a.Assumption for pooled two indep samples CI is 2 populations have same standard deviation. Look at two sample std devs and Levene's test result. Does assumption seem to hold (at 10% level)? Explain.

8. Try It! Comparing Reading scores (continued) b.Give a 95% confidence interval for the difference in the population mean reading scores.

9. Yes or No (please click in your answer) c.Based on the interval (-1.64, 13.66), does there appear to be a difference in the mean reading scores for the two populations?

10. Try It! Stroop Word Color Test Stroop Word Color Test:  100 color names shown in colors different from word.  Task = correctly identify display color of each word. Experiment:  Time to complete test for n = 16 individuals after consumed alcohol and for n = 16 other individuals after consumed placebo drink.  Each group balanced with 8 men and 8 women.

11. Ready to try it? GREEN RED BLACK BLUE

12. Try It! Stroops’ Word Color Test Assume two samples are indep random samples, Model for completion time is normal for each popul. As we go through the questions, have your clicker ready for parts (a) and (e).

13. a. What graph(s) would you make to check the normality condition? A) Make bar chart(s) B) Make qq plot(s) C) Make histogram(s) D) Make pie chart(s)

14. b.How did the two groups compare descriptively?

15. c. Which procedure? Pooled or Unpooled?

16. d.Calculate a 95% CI for the difference in popul means Think about part (e) with your clicker ready …

17. Yes or No (please click in your answer) e.Based on the interval (0.30, 27.46), can we conclude the population means for the two groups are different?