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?

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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