Question

3. Suppose the Acme Drug Company develops a new drug, designed to prevent colds. The company states that the drug is equally effective for men and women. To test this claim, they choose 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 reject the company's claim that the drug is equally effective for men and women? Use a 0.05 level of significance.

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Directions: Do 7 step hypothesis test for the following scenarios making sure to include your check of assumptions.  

Answer 1

Step 1) Null Hypothesis

Alternative Hypothesis $H1: p1\neq p2$

Step 2) Significance Level $\alpha = 0.05$

Step 3) Decision : Reject H0 if Z>1.96 or Z< -1.96

Step 4) Under H0, the test statistic is

$Z = \frac{p1-p2}{\sqrt{PQ\left ( \frac{1}{n1}+\frac{1}{n2} \right )}}$

$P = \frac{X1+X2}{n1+n2} = \frac{38+102}{100+200}= \frac{140}{300}=0.47$

$Z = \frac{0.38-0.51}{\sqrt{0.47*0.53*\left ( \frac{1}{100}+\frac{1}{200} \right )}}=-2.127$

Step 5) The P-Value is 0.03342

Step 6) Decision : Since p value is less than significance level. Reject H0

Step 7) Conclusion : YEs, we can reject the company's claim that the drug is equally effective for men and women.