EXAMPLE 7.8

Are the two means equivalent? Suppose the GE Healthcare researchers state that a mean difference less than 0.20 micron is not important. To see if the data support a mean difference within 0.00 ± 0.20 micron, we construct a 90% confidence interval for the mean difference.

The standard error is

so the margin of error is

where the critical value t* = 1.676 comes from Table D using 50 degrees of freedom. The confidence interval is

= (−0.112, 0.2133)

This interval is not entirely within the 0.00 ± 0.20 micron region that the researchers state is not important. Thus, we cannot conclude at the 5% signficance level that the two means are equivalent. Because the observed mean difference is close to zero and well within the “equivalent region,” the company may want to consider a larger study to improve precision.