[12 pts] I work for a pharmaceutical company, and I want to show that our new pill lowers cholesterol. I know that by not taking a pill there is a 0 milligram per deciliter (mg/dl) drop in blood cholesterol, with a standard deviation of = 13 mg/dl. Assume that cholesterol is normally distributed. In a random sample of 80 men taking the new cholesterol drug, I find a drop in the blood cholesterol of 3 mg/dl (x-3). I need to find out if this is a statistically significant drop. Test at the 0.05 significance level. a. What type of test are we using? We are using a one-sample test as this is appropriate for when we have a sample and want to compare the sample mean to a known population mean. This is a left-tailed test since we're interested in whether the new pill lowers cholesterol. b. Do we meet the assumptions for normality for this type of test (justify your response)