8. In order to estimate the difference in verbal SAT scores for high school stud

Question

8. In order to estimate the difference in verbal SAT scores for high school students intending to major in engineering and those intending to major in language and literature, independent random samples of size 15 were obtained from the two groups. The results were as follows Engineering F, = 446 | si = 42 Language/literature Y2 534245 a. [5] Find a 95% confidence interval estimate for the difference in verbal SAT scores between students intending to major in engineering and those intending to major in lain guage/literature. Be sure to state all assumptions required. b. [ What is the interpretation of the confidence interval in part (a) ?

Explanation / Answer

a) assuming equal variance

                            SE
Sample   N   Mean StDev Mean
1       15 446.0   42.0    11
2       15 534.0   45.0    12

Difference = (1) - (2)
Estimate for difference: -88.0
95% CI for difference: (-120.6, -55.4)
T-Test of difference = 0 (vs ): T-Value = -5.54 P-Value = 0.000 DF = 28
Both use Pooled StDev = 43.5259

confidence interval -   (-120.6, -55.4)

b) we are 95 % confident that the difference lies in this confidence interval

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