A random sample of 81 patients with end-stage renal disease gave a sample mean hemoglobin level of 10.5 g/dl with sample standard deviation 2.79 g/dl.

a)(5 pts) Calculate the Standard Error of the sample mean

b)(10 pts) Construct a 90% confidence interval for the population mean hemoglobin level based on sample data.

c)(5 pts)Interpret the confidence interval you constructed in part (b) based on the context of the problem.

d)(5 pts) Now if the researchers wish to design a new study in which the standard error of the mean will be only 0.15. How many patients need to be enrolled in the new study? Use the sample standard deviation from the preliminary data as a guess of the standard deviation.