Question

4. To test if the proportion of people with insomnia is higher among the users of a certain antidepressant as compared to such proportion among the people who do not use this treatment, a double blind experiment will be conducted on 1000 subjects randomly divided into groups. a) State the null and the alternative hypotheses. b) What is meant by a double blind study? The following are the results of the study Medication Placebo Insomnia 75 35 No Insomnia 425 465 Write the c) Test statistic d) The P_value e) Your conclusion for the above test at a 5% level of significance.

Answer 1

(a)

H0: Null Hypothesis: P1 = P2 (The proportion of people with insomnia is same among the users of a certain antidepressant as compared to such proportion among the people who do not use this treatment

HA: Alternative Hypothesis: P1 > P2 (The proportion of people with insomnia is higher among the users of a certain antidepressant as compared to such proportion among the people who do not use this treatment.

(b) Double blind is the experimental procedure in which neither the subjects nor the experimenters know which subjects are in the test and control groups during the actual course of the experiment.

(c)

n1 = 500

p1 = 75/500 = 0.15

n2 = 500

p2 = 35/500 =0.07

Q =1 - P = 0.89

SE -VPQ(1/nl1/n2)

Test statistic is:
Z = (0.15 - 0.07)/0.0198 =4.4040

So,

Test statistic is:

Z = 4.4040

(d)

Table of Area Under Standard Normal Curve gives area = 0.5 nearly

So,

P - value = 0.5 - 0.5 nearly = 0 nearly

So,

P - Value = 0.0000

Since P - Value is less than = 0.05, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that the proportion of people with insomnia is higher among the users of a certain antidepressant as compared to such proportion among the people who do not use this treatment