In a study, 129 children of a certain race in a certain city were randomly assigned to one of two groups: one group enrolled in a preschool, and the other group did not. A research question was whether attendance at preschool had an effect on high school graduation. The accompanying table shows whether the students graduated from regular high school or not and includes both boys and girls. Find a 95% confidence interval for the difference in proportions, and interpret it. Click the icon to view the data. Step 1: Calculate percentages 55 Looking at children who went to preschool, 69, or 79.7%, graduated from high school. Looking at the children who did not go to preschool, what percent graduated from high school? 56.7 % of children who did not go to preschool graduated from high school. (Round to one decimal place as needed.) Step 2: Compare In this sample, the children who attend preschool are more likely to graduate than the children who don't attend preschool. Step 3: Verify conditions Although we don't have a random sample of children, we do have random assignment to groups, and the two groups are independent. We must verify that the sample sizes are large enough. Let sample 1 be children who went to preschool and let sample 2 be children who did not go to preschool. n1P1 = 69(0.797) = 55 11 1- P1 = 69(0.203) = 14 n2P2 = 60(0.567) = 34 12 1 - P2 = 26 X Graduation data (Round to the nearest integer as needed.) Step 4: Calculate intervals Preschool No Preschool The 95% confidence interval for the difference (P, - P2) is (D). Grad HS 55 34 (Round to three decimal places as needed.) No Grad HS 14 26