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In a clinical trial, 50 patients suffering from an illness will be randomly assi

ID: 3350895 • Letter: I

Question

In a clinical trial, 50 patients suffering from an illness will be randomly assigned to one of two groups so that 25 receive an experimental treatment and 25 receive the best available treatment. The random variable Xis the response of a patient to the experimental medicine, and the random variable B is the response of a patient to the best currently available treatment. The random variables X and B are normally distributed with ,-Oz-500 under both the null and alternative distributions. The null hypothesis to be tested is that E(X) - E(B) 0against the alternative that E(X)-E(B)> 0 at the 0.01 level of significance. What is the probability of a Type II error for the test of the null hypothesis when E(x)-E(B) 500?

Explanation / Answer

Power and Sample Size

2-Sample t Test

Testing mean 1 = mean 2 (versus >)
Calculating power for mean 1 = mean 2 + difference
= 0.01 Assumed standard deviation = 500


            Sample
Difference    Size     Power
       500        25    0.866202

The sample size is for each group

type ii error = 1 - power = 1 - 0.8662 = 0.1338