Question

suppose the previous example is stated a little bit differently. Suppose the Acme Drug Company develops a new drug, designed to prevent colds. The company states that the drug is more effective for women than for men. To test this claim, they choose a a simple random sample of 100 women and 200 men from a population of 100,000 volunteers.

At the end of the study, 38% of the women caught a cold; and 51% of the men caught a cold. Based on these findings, can we conclude that the drug is more effective for women than for men? Use a 0.01 level of significance

Answer 1

P₁ = proportion of women catching cold

P₂ = proportion of men catching cold

Null hypothesis: P₁$\geq$ P₂

Alternative hypothesis: P₁ < P₂

We can conclude that the drug is more effective for women than for men if null hypothesis is rejected

Using sample data, the pooled sample proportion (p) and the standard error (SE) is calculated:

p = [(0.38 * 100) + (0.51 * 200)] / (100 + 200) = 0.467

SE = { p * ( 1 - p ) * [ (1/n₁) + (1/n₂) ] }^0.5 = [ 0.467 * 0.533 * ( 1/100 + 1/200 ) ]^0.5 = 0.061

z-score:

z = (p₁ - p₂) / SE = (0.38 - 0.51)/0.061 = -2.13

P-value:

P(z < -2.13) = 0.017

Since the P-value (0.017) is greater than the significance level (0.01), we cannot reject the null hypothesis. We can't conclude that the drug is more effective for women than for men.