Two sales scripts, equal spreads: pooled t-test

Question

Two call-center scripts are compared across reps with similar spreads, so equal variances are assumed. Script A: 20 reps, mean 12 sales, sample standard deviation 4. Script B: 18 reps, mean 15 sales, sample standard deviation 5.

Run a pooled two-sample t-test at the 5% level (two-sided): do the mean sales 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{19(16) + 17(25)}{36} = \frac{304 + 425}{36} = \frac{729}{36} = 20.25. So sp = 4.5. Standard error of the difference: 	ext{SE} = 4.5\sqrt{\frac{1}{20} + \frac{1}{18}} = 4.5\sqrt{0.10556} = 4.5(0.3249) = 1.462. Test statistic: t = \frac{12 - 15}{1.462} = \frac{-3}{1.462} = -2.05. Degrees of freedom: 20 + 18 - 2 = 36; the two-sided 5% critical value is t{0.025,\,36} \approx 2.028. Since -2.05 = 2.05 2.028, reject H0 (just barely). The p-value is about 0.047. Conclusion: there i…

Two sales scripts, equal spreads: pooled t-test

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