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 ?nal exam are shown in the following table.
|
Average
|
58
|
69
|
55
|
65
|
88
|
52
|
99
|
76
|
45
|
86
|
55
|
79
|
|
Gifted
|
77
|
86
|
84
|
93
|
77
|
91
|
87
|
95
|
68
|
78
|
74
|
58
|
(a) Compute the 95% con?dence interval on the difference between the mean of the students being taught by this new method.
(b) Construct a 95% con?dence interval for the ratio of variance in test scores for regular and gifted students, σ2/σ2.
1 2
(c) What are the assumptions you made in parts (a) and (b)? Are these assumptions justi?ed?