Question: A drug company wishes to test its new medication to lower glucose levels in diabetics. If the adult US diabetic population has glucose level \(\mu \) = 130 mg/dl with \(\sigma \) = 30 mg/dl; and, in pilot studies the new drug appears to reduce glucose levels to 120 mg/dl. The company wishes to test the drug against placebo using n = 25, and a Type I error of 5%. As a result, given the SDOM (sample distribution of means) for N=25, the company will need to attain a sample mean \(\bar{X}\) = 120.13 in order to reject the null hypothesis. Suppose that, in fact, sample mean = 120. The company rejects the null hypothesis and accepts the alternate. How powerful will the test be? Is the value obtained satisfactory?

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