A drug company is testing a drug intended to lower A1C in prediabetic patients. For the decrease to be clinically meaningful, the company needs to show a mean decrease of more than 0.3. A random...

A drug company is testing a drug intended to lower A1C in prediabetic patients. For the decrease to be clinically meaningful, the company needs to show a mean decrease of more than 0.3. A random sample of 20 prediabetic patients shows a mean decrease of 0.35. Suppose that we know σ = 0:4:

(a) Using a significance level of α = 5%, can the company show a meaningful decrease?

(b) Before marketing the drug, the company wants very strong evidence of a meaningful decrease. In that case, should they use α = 1% or α = 10%?