EXAMPLE 7.19

Does increased calcium reduce blood pressure? Take Group 1 to be the calcium group and Group 2 to be the placebo group. The evidence that calcium lowers blood pressure more than a placebo is assessed by testing

H₀: μ₁ = μ₂

H_a: μ₁ >μ₂

Here are the summary statistics for the decrease in blood pressure:

The calcium group shows a drop in blood pressure, and the placebo group has a small increase. The sample standard deviations do not rule out equal population standard deviations. A difference this large will often arise by chance in samples this small. We are willing to assume equal population standard deviations. The pooled sample variance is

so that

The pooled two-sample t statistic is

The P-value is , where T has the distribution.

From Table D, we can see that P falls between the and levels. Statistical software gives the exact value . The experiment found evidence that calcium reduces blood pressure, but the evidence falls a bit short of the traditional 5% and 1% levels.