Question

taking the drug. The study included 9807 overweight or obese subjects with pre-existing cardiovascular disease and/or type 2 diabetes. The subjects were randomly assigned to (4908 subjects) or a placebo (4899 subjects) ) in a double-blind fashion. The primary outcome measured was the occurrence of any of the following events: nonfatal a myocardial infarction or stroke, resuscitation after cardiac arrest, or cardiovascular death. The primary outcome was observed in 561 subjects in the subitramine group and 493 subjects in the placebo group Do the data give good reason to think that there is a difference between the proportions of treatment and placebo subjects who experienced the primary outcome? (Note that sibutramine has not been available in the United States since the end of 2010 due to its manufacturer's concerns over increased risk of heart attack or stroke, although at the present time it can still be purchased in other countries.) State hypotheses, find the test statistic, and the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) Ho: Ptreatment2Pplacebo State your conclusion. (Use α 0.05.) O Because the P-value ls large, we have evidence that there is a difference in the proportion of-primary outcomes" between subitramine and placebo. O Because the P-value is small, we have evidence that there is a difference in the proportion of "primary outcomes" between subitramine and placebo. O Because the P-value is small, we do not have evidence that there is a difference in the proportion of "primary outcomes" between su O Because the P-value is large, we do not have evidence that there is a difference in the proportion of "primary outcomes" between su bitramine and placebo.

Answer 1

The statistical software output for this problem is:

Two sample proportion summary hypothesis test:
p₁ : proportion of successes for population 1
p₂ : proportion of successes for population 2
p₁ - p₂ : Difference in proportions
H₀ : p₁ - p₂ = 0
H_A : p₁ - p₂ ≠ 0

Hypothesis test results:

Difference	Count1	Total1	Count2	Total2	Sample Diff.	Std. Err.	Z-Stat	P-value
p1 - p2	561	4908	492	4899	0.01387452	0.0062523513	2.2190883	0.0265

Hence,

Ho: p_treatment = p_placebo

Ha: p_treatment $\neq$ p_placebo

z = 2.22

P - value = 0.0265

Conclusion: Option B is correct.