Two teaching methods, equal spreads: pooled t-test

Question

Two teaching methods are compared on separate groups of students with similar score spreads, so equal variances are assumed. Method A: 15 students, mean 82, sample standard deviation 10. Method B: 15 students, mean 73, sample standard deviation 8.

Run a pooled two-sample t-test at the 5% level (two-sided): do the mean scores differ? Report the t-statistic.

Accepted Answer

Equal variances assumed, so pool. Hypotheses: H0: \muA = \muB versus H1: \muA 
eq \muB. Pooled variance: sp^2 = \frac{14(100) + 14(64)}{28} = \frac{1400 + 896}{28} = \frac{2296}{28} = 82. So sp = 9.055. Standard error of the difference: 	ext{SE} = 9.055\sqrt{\frac{1}{15} + \frac{1}{15}} = 9.055\sqrt{0.13333} = 9.055(0.3651) = 3.306. Test statistic: t = \frac{82 - 73}{3.306} = \frac{9}{3.306} = 2.72. Degrees of freedom: 15 + 15 - 2 = 28; the two-sided 5% critical value is t{0.025,\,28} = 2.048. Since 2.72 2.048, reject H0. The p-value is about 0.011. Conclusion: there is evidence method A pr…

Two teaching methods, equal spreads: pooled t-test

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