Question

Zoloft is a drug used to treat obsessive-compulsive disorder (OCD). In randomized, double-blind clinical trials, 926 patients diagnosed with OCD were randomly divided into two groups. Subjects in group 1 (experimental group) received 200 milligrams per day (mg/day) of Zoloft, while subjects n group 2 (control group) received a placebo. Of the 553 subjects in the experimental group, 77 experienced dry mouth as a side effect. Of the 373 subjects in the control group, 34 experienced dry mouth as a side effect. Do a higher proportion of subjects experience dry mouth who are taking Zoloft versus the proportion taking the placebo? Use the α = 0.01 level of significance. Use the p-value approach

- 1,Requirements?

-2,Hypothesis test?

Answer 1

Answer:

Given,

Ho : p1-p2 <= 0

Ha : p1-p2 > 0

sample proportion p1^ = x1/n1 = 77/553 = 0.139

p2^ = x2/n2 = 34/373 = 0.091

p = (x1+x2)/(n1+n2)

substitute values

= (77 + 34)/(553 + 373)

= 0.1199

Pooled standard error = sqrt(pq(1/n1 + 1/n2))

substitute values

= sqrt(0.1199(1-0.1199)(1/553 + 1/373))

= 0.022

test statistic z = (p1^ - p2^)/se

substitute values

= (0.139 - 0.091)/0.022

= 2.18

P value = P(z > 2.18)

= 0.0146287 [since rom z table]

= 0.0146

Here we observe that, p value < alpha, so we reject Ho.

So there is sufficient evidence to conclude that p1 > p2.