Suppose there are two elementary schools in a county. One school (A) loans all its students a laptop computer for use in classes. The other (B) does not. We would like to compare performance on a standardized test for the two groups of students.
There are 28 students randomly chosen from school A and 34 from school b. The average test score for A is 78, and for B is 75. The sample standard deviation for A is 7 and for B is 10. While the population variances are unknown, we will assume they are equal.
a. What is the 99% confidence interval for the difference between the two school's scores. (For consistency, let the difference d=A-B.)
b. Suppose we want to perform a two-tailed test where H0 is that μd=0. What is (approximately) the p-value of the test?