EXAMPLE 7.22

Planning a new blood pressure study. In Example 7.20 (page 452), we calculated a 90% confidence interval for the mean difference in blood pressure. The 90% margin of error was roughly 5.6 mm Hg. Suppose that a new study is being planned and the desired margin of error at 90% confidence is 2.8 mm Hg. How many subjects per group do we need?

The pooled sample standard deviation in Example 7.20 is 7.385. To be a bit conservative, we’ll guess that the two population standard deviations are both 8.0. To compute an initial n, we replace t* with z*. This results in

We round up to get n = 45. The following table summarizes the margin of error for this and some larger values of n.

The requirement is first satisfied when n = 47. In SAS, we’d perform these calculations using the command

proc power;

twosamplemeans CI=diff alpha=0.1 stddev=8 halfwidth=2.8

probwidth=0.50 npergroup=.;

run;

This sample size is roughly 4.5 times the sample size used in Example 7.20. This researcher may not be able to recruit this large a sample. If so, we should consider a larger margin of error.