Does the drug beat placebo on recovery?

Question

In a clinical trial, 130 of 200 patients recover on a new drug (65%) while 110 of 200 recover on placebo (55%).

Test at the 5% level (two-sided) whether the true recovery rates differ, using a pooled two-proportion z-test, and report the z-statistic.

Accepted Answer

Hypotheses: H0: p{	ext{drug}} = p{	ext{placebo}} versus H1: p{	ext{drug}} 
eq p{	ext{placebo}}. Sample proportions: \hat p{	ext{drug}} = 0.65, \hat p{	ext{placebo}} = 0.55. Pooled proportion: \hat p = \frac{130 + 110}{200 + 200} = \frac{240}{400} = 0.60. Standard error under the null: 	ext{SE} = \sqrt{0.60 	imes 0.40 	imes \left(\frac{1}{200} + \frac{1}{200}ight)} = \sqrt{0.24 	imes 0.01} = \sqrt{0.0024} = 0.04899. Test statistic: z = \frac{0.65 - 0.55}{0.04899} = \frac{0.10}{0.04899} = 2.04. Since 2.04 1.96, reject H0 (just barely). The two-sided p-value is about 0.041. Conclusi…

Does the drug beat placebo on recovery?

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