Two diets, equal spreads: pooled t-test

Question

Two diets are compared on separate groups with similar spreads, so equal variances are assumed. Diet 1: 12 people, mean loss 4.5 kg, sample standard deviation 1.5. Diet 2: 10 people, mean loss 3.0 kg, sample standard deviation 1.2.

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

Accepted Answer

Equal variances assumed, so pool. Hypotheses: H0: \mu1 = \mu2 versus H1: \mu1 
eq \mu2. Pooled variance: sp^2 = \frac{11(2.25) + 9(1.44)}{20} = \frac{24.75 + 12.96}{20} = \frac{37.71}{20} = 1.8855. So sp = 1.373. Standard error of the difference: 	ext{SE} = 1.373\sqrt{\frac{1}{12} + \frac{1}{10}} = 1.373\sqrt{0.18333} = 1.373(0.4282) = 0.5879. Test statistic: t = \frac{4.5 - 3.0}{0.5879} = \frac{1.5}{0.5879} = 2.55. Degrees of freedom: 12 + 10 - 2 = 20; the two-sided 5% critical value is t{0.025,\,20} = 2.086. Since 2.55 2.086, reject H0. The p-value is about 0.019. Conclusion: there is evi…

Two diets, equal spreads: pooled t-test

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