4. [13 marks] A research study is done to assess the LDL cholesterol in patients receiving either a placebo or 80 mg/d simvastatin. The placebo group had 23 people and the simvastatin had 19 people. After 24 months the mean LDL cholesterol level is found to be 81 mg/dL with standard deviation of 46 mg/dL for the placebo group and the mean LDL cholesterol level and standard deviation for the simvastatin group were 66 mg/dL with a standard deviation of 54 mg/dL. a) Compare the two groups by calculating the 95% confidence interval for both groups for their mean LDL cholesterol. b) Determine if there is a significant difference between the mean LDL cholesterol for the two groups using a formal hypothesis test. Use 95% confidence. 1. [ 4 marks] Explain clearly what the Central Limit Theory tells us about large samples taken from a population of subjects. The population is known to have a mean of 34 and a standard deviation of 7? Consider cases samples size equals 1 and >1