A controlled clinical trial was run to investigate the effect of the drug stelazine on chronic schizophrenics. The trials were conducted on chronic schizophrenics in two closed wards. In each of the wards, the patients were divided into two groups matched for age, length of time in the hospital, and disease severity as measured by a behavior rating score. One member of each pair was given stelazine, and the other a placebo. Only the hospital pharmacist knew which member of each pair received the actual drug.

The data is given in the spreadsheet (attached) and shows, for each of the patients, the change in the patient's behavioral rating score after 3 months. Positive values indicate an improvement in the patient's behavior over the three month period, while negative values indicate that the patient's behavior declined. The table also shows the difference between the stelazine patient's change and placebo patient's change for each of the patient pairs.
Use appropriate hypothesis tests to answer the following two problems, being sure to complete each of the four steps:

i. state the two hypotheses being tested (be sure to define any parameters used, if they were not defined previously),
ii. compute the appropriate test statistic, degrees of freedom (if applicable), and p-value,
iii. decide whether to reject the null hypothesis when using a significance level of 0.05, and
iv. conclude by writing a short sentence describeing what your decision means in the context of the problem.

Please answer the following:
a. Considering all patients, test whether the average behavioral change is higher for patients using stelazine than for patients receiving a placebo (thus indicating that stelazine improves chronic schizophrenic behavior).
b. Using the differences, S-P, test whether stelazine is more effective, on average, in one of the wards than in the other. Carry out the appropriate test for the equality of variances if necessary. Were we right to combine all patients for our answer in (a)?