Does the drug cure more than 60% of cases?

Question

A drug is worth pursuing only if it cures more than 60% of cases. In a trial of 150 patients, 99 are cured (66%).

Run a one-sided one-proportion z-test at the 5% level (is the cure rate above 60%?): report the z-statistic and the decision.

Accepted Answer

Directional claim (above 60%), so use an upper-tail test. Hypotheses: H0: p = 0.60 versus H1: p 0.60. Sample proportion: \hat p = 99/150 = 0.66. Standard error under the null (p = 0.60): 	ext{SE} = \sqrt{\frac{0.60 	imes 0.40}{150}} = \sqrt{0.0016} = 0.04. Test statistic: z = \frac{0.66 - 0.60}{0.04} = \frac{0.06}{0.04} = 1.5. The one-sided 5% critical value is 1.645. Since 1.5 < 1.645, we fail to reject H0. The one-sided p-value is 1 - \Phi(1.5) \approx 0.067. Conclusion: the observed 66% is encouraging but not significant; the trial is too small to confirm the cure rate exceeds 60%. Takea…

Does the drug cure more than 60% of cases?

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