In a clinical trial of 2029 subjects treated with a certain​ drug, 22 reported headaches. In a control group of 1572 subjects given a​ placebo, 26 reported headaches. Denoting the proportion of headaches in the treatment group by pt and denoting the proportion of headaches in the control​ (placebo) group by pc​, the relative risk is pt​/pc. The relative risk is a measure of the strength of the effect of the drug treatment. Another such measure is the odds​ ratio, which is the ratio of the odds in favor of a headache for the treatment group to the odds in favor of a headache for the control​ (placebo) group, found by evaluating StartFraction p Subscript t Baseline divided by left parenthesis 1 minus p Subscript t Baseline right parenthesis Over p Subscript c Baseline divided by left parenthesis 1 minus p Subscript c Baseline right parenthesis EndFractionpt/1−ptpc/1−pc. The relative risk and odds ratios are commonly used in medicine and epidemiological studies. Find the relative risk and odds ratio for the headache data. What do the results suggest about the risk of a headache from the drug​ treatment?

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2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.