3. (22 points total) A pharmaceutical company claims to have developed a drug that simultaneously reduced cholesterol levels in the human body and causes weight loss. A random sample of n = 30 individuals from a population of patients is obtained, and each individual's change in cholesterol level (Xi) and body weight (X2) are recorded after taking the new drug for a year. Assume X' : and X's follow a bivariate normal distribution jointly. The sample mean vector and sample variance-covariance matrix are given as Let /1 and /2 be the average cholesterol level change and the average weight change, respectively, for the population of patients after taking the new drug for a year. a. (8 pt) Construct a 95% Hoteling's T confidence region for # = (uni. /2)'. Note: Present the region in a quadratic form is sufficient, do NOT need to draw the confidence region. b. (10 pt) At a level of significance of 0.05, can you conclude that the new drug has an impact (in either direction) on the population mean cholesterol level and/or body weight? State your hypotheses, the test statistic to be used, the Hoteling's 7 rejection region, your work towards a statistical decision and finally, your conclusion. c. (4 pt) Can you use the confidence region that you have determined in part (a) to conduct the test in part (b)? What final conclusion can you draw if you use the confidence region in part (a) to conduct the test in part (b)? Explain your answers in details