A pharmaceutical company has developed a new drug to reduce cholesterol. A regulatory agency will recommend the new drug for use if there is convincing evidence that the mean reduction in cholesterol level after one month of use is more than 20 milligrams/deciliter (mg/dl), because a mean reduction of this magnitude would be greater than the mean reduction for the current most widely used drug.

The pharmaceutical company collected data by giving the new drug to a random sample of 50 volenteers having high cholestrol. The reduction in cholestrol level after one month was recorded for each individual, resulting in a sample mean reduction of 24 mg/dl and a standard deviation of 15 mg/dl.

(a) The regulatory agency decided o use a confidence interval estimate for the population mean reduction in cholestrol level for the new drug. Provide a 95% confidence inerval for the mean reduction in cholestrol level.