culate inte Graduation Data onfidence in three decima aw Conclus al Preschool No Preschool Grad HS 51 35 No Grad HS 17 34 ☑ 13 The dala In a study, 137 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 51 Looking at children who went to preschool, or 75.0 %, graduated from high school. Looking at the children who did not go to preschool, what percent graduated from high school? 68' % 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 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. (1-1)-6810.250)=17 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. n₁₁ = 68(0.750)=51 Questi nd a 95% confidence Click the icon to preschool had an in race ins In a study, 137 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 4: Calculate intervals The 95% confidence interval for the difference (P₁ - P2) is (☐☐). (Round to three decimal places as needed.) Step 5: Draw Conclusions The interval Step 6: Generalize 0, suggesting that it plausible that the proportions are the same. Can we generalize to a larger population from this data set? Why or why not? generalize to a larger population from this data set, since this study Step 7: Determine causation Can we conclude from this data set that preschool caused the difference? Why or why not? conclude from this data set that the preschool caused the difference, since this study