A study of 102 patients who had digestive-tract surgery found that those who chewed a stick of gum for 15 minutes at mealtimes ended up being discharged after an average of 4.4 days in the hospital, compared to an average of 5.2 days for their counterparts who were not provided with gum.
Assuming (1) a sample size of 51 for each group and (2) sample standard deviations of 1.3 and 1.9 days, respectively, use a z-test and the 0.01 level of significance in examining whether the mean hospital stay for the gum-chewing patients could have been this much lower simply by chance.
Determine and interpret the p-value for the test.