Rosenthal and Jacobson (1968) informed classroom teachers that some of their students showed unusual potential for intellectual gains. Eight months later the students identified to teachers as having potentional for unusual intellectual gains (Experimental) showed significiantly greater gains performance on a test said to measure IQ than did children who were not so identified (Comparison). The mean scores for both set of students were recorded. Below is the results from the t-test: 1 a What was the estimated mean gain in performance for the students who were considered to have potential to make intellectual gains (i.e. Group 1 - Experimental) ? b What is the estimated mean difference between the students who were considered to have potential to make gains (Group 1 - Experimental) and the students who were not identified (Group 2 - Comparison)? c State the null and alternative hypothesis in the context of this study. d State the observed test-statistic, and the associated p-value. Further, make a conclusion based on the p-value. e State the 95% CI for the difference between the means between Group 1 - Experimental and Group 2 - Comparison. Interpret this interval. f Suppose we increased the same size to 1000 students, 500 students in each group. How would this change the interval in part (f)

Group Statistics Std. Error group N Mean Std. Deviation Mean SCT 20 27.15 12.508 2.797 2 20 11.95 14.612 3.267 Independent Samples Test scr Equal variances Equal variances assumed not assumed Levene's Test for F 1.877 Equality of Variances Sig. .179 t-test for Equality of t 3-534 3-534 Means df 38 37.117 Sig. (2-tailed) .001 .001 Mean Difference 15-200 15.200 Std. Error Difference 4.301 4.301 95% Confidence Interval Lower 6.493 6.486 of the Difference Upper 23-907 23.914