An experiment is conducted comparing the effectiveness of a new method of teaching algebra for eighth-grade students. Twelve gifted and 12 regular students are taught using this method. Their scores on a final exam are shown in the following table.

(a) Compute the 95% confidence interval on the difference between the mean of the students being taught by this new method.
(b) Construct a 95% confidence interval for the ratio of variance in test scores for regular and gifted students, σ12 / s22.
(c) What are the assumptions you made in parts (a) and (b)? Are these assumptions justified?

Average Gifted 58 69 55 65 88 52 99 76 45 86 55 79 86 84 93 77 9 87 95 68 78 74 58