[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. [ 15 marks] In trying to correct for patient size in radiation dose calculations for cardiology a relationship between dose area product (DAP) in (Gy-cm) and patient weight (kg) needs to be determined; the variation is expected to be linear. The following data was taken: DAP (Gy-cm) Weight (kg) 22 50 13- 55 14 . 64 16 . 76 12 80 14. 95 11 112 DAP =102 DAP? = 1566 [WEIGHT = 532 = 2x [ DAP .WEIGHT = 7449 [ WEIGHT? = 43366 = 2x a) Find the equation of the best fit line. Think carefully about which should be the independent variable. b) Determine if you think a linear relationship is valid using appropriate calculations. c) If the patient's weight is 70 kg, find the required DAP along with a 90% confidence (prediction) interval