Answered

For each part of this problem, show all your work and write a probability statement.
Investigators recently reported the results a study designed to assess whether or not the herb, St. John’s Wort is effective in treating moderately severe cases of depression. The study involved 338 subjects, randomly assigned to receive one of three treatments: St. John’s Wort, Zoloft, or a placebo. The authors were primarily interested in whether St. John’s Wort performed better than placebo and included Zoloft as a "way to measure how sensitive the trial was to detecting antidepressant effects." Their results are presented in the table below:
St. John's Wort Placebo Zoloft Total
Full Response 27 37 27 91
Partial Response 26 13 26 55
No Response 70 66 56 192
Total 113 116 109 138
1. What is the probability that a randomly selected subject had no response?
2. What is the probability that a randomly selected subject was treated with Zoloft and had a full response?
3. What is the probability that a randomly selected subject had a full or partial response given they were treated at St. John's Wort?
4. What is the probability that a randomly selected subject who didn't have a full response was treated with Placebo?

Answer :

Answer:

Follows are the answer to the given point.

Step-by-step explanation:

In point 1:

[tex]\to P( \text{number of response}) = \frac{192}{338} \\[/tex]

                                        [tex]= \frac{96}{169}\\\\= 0.56[/tex]

In point 2:

[tex]\to P| \text{(Zoloft and fill response)}| = \frac{27}{338}[/tex]

                                                 [tex]= 0.079[/tex]

In point 3:

[tex]\to P(\frac{\text{ full or partial}}{\text{St. John's Wort}}) = \frac{\frac{43}{338}}{\frac{113}{338}}[/tex]

                                [tex]= \frac{43}{338} \times \frac{338} {113}\\\\= \frac{43}{113}\\\\= 0.38[/tex]

In point 4:

[tex]\to P(\frac{\text{Placebo}}{\text{full or response}}) = P(\frac{(\text{Placebo} \cap \text{full or response})} {\text{p(full response)}})[/tex]

                               [tex]= \frac{\frac{79}{338}}{ 1- \frac{91}{338}} \\\\ = \frac{\frac{79}{338}}{ \frac{338-91}{338}} \\\\ = \frac{\frac{79}{338}}{\frac{247}{338}} \\\\ = \frac{79}{338} \times \frac {338}{247} \\\\= \frac{79}{274} \\\\ = 0.28[/tex]

Other Questions