Did the drug lower blood pressure?

Question

A trial measures systolic blood pressure in 15 patients before and after a drug. For each patient, compute the reduction (before minus after, in mmHg). The reductions have a mean of 6 mmHg and a sample standard deviation of 10 mmHg.

Run a paired t-test at the 5% level (two-sided): did the drug change blood pressure? Report the t-statistic.

Accepted Answer

Each patient is measured twice, so the data are paired. Work with the differences di and run a one-sample t-test with 15 - 1 = 14 degrees of freedom. Hypotheses: H0: \mud = 0 versus H1: \mud 
eq 0. Standard error: 	ext{SE} = \frac{sd}{\sqrt{n}} = \frac{10}{\sqrt{15}} = \frac{10}{3.873} = 2.582 	ext{ mmHg}. Test statistic: t = \frac{6}{2.582} = 2.32. The two-sided 5% critical value for 14 degrees of freedom is t{0.025,\,14} = 2.145. Since 2.32 2.145, reject H0. The p-value is about 0.036. Conclusion: the drug significantly lowered blood pressure, by about 6 mmHg on average. Takeaway. Patien…

Did the drug lower blood pressure?

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