full step please

Problem 2 [24 points]: Consider a new proposed antibiotic is taken by 16 patients, and their serum-creatinine level are measured 24 hours after. Assume that the serum-creatinine level is normally distributed, and the sample mean of serum-creatinine level was 1.50 mg/dL and sample variance of serum-creatinine level was 0.0784. Suppose that the standard deviation of serum-creatinine level in population is known at 0.28 mg/dl. (a) [3 points] Construct a 95% Confidence Interval for the mean serum-creatinine level . (b) [4 points] Instead of using the Zo,oas = -1.96 and Zo.97s =1.96 to construct the 95% Confidence Interval for / in part (a), construct another 95% Confidence Interval for u based on Zo.as and Zo.gy (i.e. 2d and 97th percentile of N (0,1)). (c) [4 points] Compare part (b) to part (a), what's the difference between these two confidence intervals? Which confidence intervals provide a more accurate estimation? Why? [Why we commonly use Symmetry setting (Za/2 and Z,-a/2) in confidence interval?] (d) [4 points] if we want to control the width of 90% confidence interval for / is less than 0.5 (Margin of Error is less than 0.25), what's the minimum value of the sample size n we should collect? Suppose that the standard deviation of serum-creatinine level in population is unknown (e) [5 points] Construct a 98% Confidence Interval for the mean of serum-creatinine level u and a 98% Confidence Interval for the Variance of serum-creatinine level o based on the sample mean and sample variance. (f) [4 points] Construct a 95% Confidence Interval for the mean serum-creatinine level and compare it to the Confidence Intervals in Part (a), which Confidence Intervals are more accurate, why