Say a scholarship is randomly assigned to a subset of students (treated) and not to others (control). The two groups are ex-ante identical and the sample size is 10,000. Assume this sample size is large enough such that a normal approximation is appropriate. The average score of the treated group is 10 and the average score of the control group is 9.2. The variance of difference between the treated and control is 0.25 and the 95% critical value for normal approximation is 1.96.
1. Compute the 95% confidence interval of the effect of the scholarship on student performance.