EXAMPLE 7.8 Are the Two Means Equivalent?

Suppose the GE Healthcare researchers state that a mean difference less than 0.25 microns is not important. To see if the data support a mean difference within microns, we construct a 90% confidence interval for the mean difference.

The standard error is

so the margin of error is

where the critical value comes from Table D using the conservative choice of 60 degrees of freedom.

The confidence interval is

This interval is entirely within the micron region that the researchers state is not important. Thus, we can conclude at the 95% confidence level that the two means are equivalent. The company can turn this option off to save time obtaining measurements.