Question

2. An article in the Journal of the American Medical Association reports the results of a

study designed to see if the herb St. John's wort is effective in treating moderately
severe cases of depression. The study involved 338 patients who were being treated
for major depression. The subjects were randomly assigned to receive one of three
treatments: St. John's wort, Zoloft (a prescription drug), or placebo (an inactive
treatment) for an 8-week period. The two way table summarizes the data from the
experiment
Treatment
a. What proportion of subjects in the study were
St. John's
randomly assigned to take St. John's wort?
wort Zoloft Placebo
Explain why this value makes sense.
Full
27 27
The proportion of subjects in the study that were randomly assigned
response
to take St. John's wort is about 1/3 (113/338).
Change in Partial
16 26 13
depression response
No
70 56 66
b. Find the distribution of change in depression
response
for the subjects in this study using relative
frequencies.
37
1
C. What percent of subjects took Zoloft and showed a full response?

Answer 1

a. 113/338

b. The relative frequency distribution is presented as follows;

`{}` St. John's wort Zoloft Placebo

Full response
`{}` 27/91 27/91 37/91

Partial response
`{}` 16/55 26/55 13/55

No response
`{}` 35/96 7/24 11/32

c. 29.67%

Explanation:

a. The proportion of subjects assigned to take St. John wort is found as follows;

The total number of subjects = 27 + 27 + 37 + 16 + 26 + 13 + 70 + 56 + 66 = 338 subjects

The number of subjects assigned to take St. John wort = 27 + 16 + 70 = 113

The proportion of subjects assigned to take St. John wort = 113/338

b. The distribution of change in depression response using relative frequency is found as follows;

Total full response = 27 + 27 + 37 = 91

Total partial response = 16 + 26 + 13 = 55

No response = 70 + 56 + 66 = 192

`{}` St. John's wort Zoloft Placebo

Full response
`{}` 27/91 27/91 37/91

Partial response
`{}` 16/55 26/55 13/55

No response
`{}` 35/96 7/24 11/32

c. The percentage of subjects that took Zoloft and showed full response is given as follows;

The percentage of subjects that took Zoloft and showed full response = 27/91 × 100 = 29.67%