Question

a sample of 200 persons with a particular disease was selected out of these, 100 were given a drug and the others were not given any drug. that cured number of persons who had drug were 65 and had no drug were 55. those who were not cured and had drug were 35 and had no drug were 45. test whether the drug is effective or not.

Answer 1

solution

Proportion of cured with drug

$$p_d= \frac{65}{100}=0.65$$

Proportion of cured without drug

$$p_c= \frac{55}{100}=0.55$$

we test the hypothesis that the two sample proportions are the same.

$$Z = \frac{(p_d-p_c)-0}{ \sqrt{p(1-p)(\frac{1}{n_1}+\frac{1}{n_2})}}$$

Where $p$ is the proportion of cured from both samples combined.

$$p = \frac{65+55}{200}=0.6$$

$$Z = \frac{(0.65-0.55)-0}{ \sqrt{0.6(1-0.6)(\frac{1}{100}+\frac{1}{100})}}= 1.4434$$

At a $95\%$ level of confidence, we reject the hypothesis that the sample proportions are the same if the Z score exceeds $1.96$ .

answer: Since $1.4434<1.96$ we conclude that the drug is not effective