The following are the final grades of two sections of one statistics course. n1=22 students in section 1 have a sample of an average of x1 = 84 with a standard deviation of s1 = 4. n2=18 students in section 2 made a sample average of x2 = 80 with a standard deviation of s1 = 6. We now want to assess the difference of population means 1 2 of grades between two sections.

(1) (15 points) Test for H0 : 1 2 = 0 v.s. Ha : 1 2 = 0 using a large sample Z-test and report the p value. Use a significance level of = 0.025.

(2) (10 points) Compute a 95% confidence interval estimate for 1 2.