Test the hypothesis for difference between two mean and find out the 99% confidence interval for two mean.
Hypersexual behaviour caused by traumatic brain injury (TBI) is often treated with drug DepoProvera. In one clinical study, eight young male TBI patients who exhibited hypersexual behaviour were treated weekly with 400 mgs of DepoProvera for six months. The testosterone levels [in ng/DL] prior to treatment and at the end of the 6month treatment period are given in the table below.
Patient

PreTreatment

After 6 months on DepoProvera

1 2 3 4 5 6 7 8

849 903 890 1,092 362 900 1,006 672

96 41 31 124 46 53 113 174

a. find out a 99 percent confidence interval for the true mean difference between pretreatment and after treatment testosterone levels of young male TBI patients.
b. Perform; using the usual 4 steps, a test of hypothesis to determine if the treatment by DepoProvera is effective in reducing testosterone levels of young male TBI patients. Utilize α = 0.5.