The article "Treadmill Exercise and Resistance Training in Patients With Peripheral Arterial Disease With and Without Intermittent Claudication. A Randomized Controlled Trial" (M. McDermott, P. Ades, et al., Journal of the American Medical Association, 2009:165-174) reported the results of a study to determine whether treadmill exercise could improve the walking ability of patients suffering from claudication, which is pain caused by insufficient blood flow to the muscles of the legs. A sample of 48 patients walked on a treadmill for six minutes every day. After six months, the mean distance walked in six minutes was \(348 \mathrm{~m}\), with a standard deviation of \(80 \mathrm{~m}\). For a control group of 46 patients who did not walk on a treadmill, the mean distance was \(309 \mathrm{~m}\) with a standard deviation of \(89 \mathrm{~m}\). Find a \(95 \%\) confidence interval for the difference in mean distance walked between the two groups of patients.