Did the typing course raise words per minute?

Question

A typing course tests the same 10 students before and after. For each student, compute the gain (after minus before, in words per minute). The gains have a mean of 8 wpm and a sample standard deviation of 15 wpm.

Run a paired t-test at the 5% level (two-sided): did the course change typing speed? Report the t-statistic.

Accepted Answer

Paired data (each student measured twice), so use the differences di with a one-sample t-test on 10 - 1 = 9 degrees of freedom. Hypotheses: H0: \mud = 0 versus H1: \mud 
eq 0. Standard error: 	ext{SE} = \frac{sd}{\sqrt{n}} = \frac{15}{\sqrt{10}} = \frac{15}{3.162} = 4.743 	ext{ wpm}. Test statistic: t = \frac{8}{4.743} = 1.69. The two-sided 5% critical value for 9 degrees of freedom is t{0.025,\,9} = 2.262. Since 1.69 = 1.69 < 2.262, we fail to reject H0. The p-value is about 0.13. Conclusion: the 8 wpm average gain is not significant; the improvements are too variable across students to r…

Did the typing course raise words per minute?

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