A study of a new anti-depressant drug took a sample of 10 individuals with high depression screening measures (DSM) and gave them the drug for three months. At the end of the three months the depression screening measure was calculated for each individual again. The results are given below:
|
DSM before taking the drug
|
7.9
|
8.3
|
9.1
|
8.2
|
8.7
|
9.4
|
9
|
8.9
|
8.7
|
9.1
|
|
DSM after three months taking the drug
|
8.1
|
7.8
|
7.3
|
7.9
|
8.1
|
7.2
|
8.3
|
7.2
|
9.3
|
7.1
|
The DSM is bases on a 10 point scale with higher numbers indicating more severe symptoms of depression.
A) What statistical procedure would you use to determine if we can conclude that the drug is effective in reducing the symptoms of depression?
B) Determine if the requirements are met for us to use this procedure. Explain how you arrive at your decision.
C) Regardless of whether the requirements are satisfied, find a 95% confidence interval for the average amount a person's DSM score changes after using the drug for three months.
D) What would be the null and alternative hypothesis for the test you would use to determine if the drug, on average, decreases individual's DSM scores?
E) What is the test statistic (give the actual numeric value of the test statistic as well as its name) for this hypothesis test?
F) What is the p-value for this test?
G) What is your conclusion (in both statistical jargon and in plain English)?