Example 137

Example 137:  A study was done to determine the effects of a 6-day administration of growth hormone on strength gains in men who perform the bench press.  Two groups of men were randomly selected for the study.  Twenty-five of them were placed into the (placebo) control group.  Twenty-three of the men were given a six-day dose of growth hormone (19 mcg/kg/d).  On day one of the study strength in the maximum bench press was recorded for each subject, and it was shown that the two groups were not significantly different from each other at that point in the study.  Seven days after the last of the growth hormone injections were administered, strength in the maximum bench press was recorded again.  The control group had an average max bench of 220 pounds and a standard deviation of 24 pounds.  The growth hormone group had an average max bench press of 251 pounds with a standard deviation of 18 pounds.  Construct a 98% confidence interval estimate of the difference between the mean max bench press for the two groups (assume maximum bench press is a normally distributed random variable and do not assume equal variances).  Does there appear to be a significant difference between the strength of the two groups?