A medical research team conducted a study to test the effect of a migraine drug. In the study, 400 subjects took the drug and 407 subjects took a placebo. The results after two hours are shown below. At α = 0.05, can you reject the claim that the proportion of subjects who are pain-free is the same for the two groups?

Are You Pain-Free After Two Hours?

(a) Identify the claim and state H₀ and H_a,

(b) Find the critical value(s) and identify the rejection region(s),

(c) Find the standardized test statistic z,

(d) Decide whether to reject or fail to reject the null hypothesis,

(e) Interpret the decision in the context of the original claim. Assume the samples are random and independent. If convenient, use technology.

Yes 41 Yes No 100 300 No 366 Drug Placebo