Confidence interval for the population mean.

Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma. Over a period of months, an adult male patient has taken eight blood tests for uric acid. The mean concentration was x = 5.35 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal with σ = 1.85 mg/dl.

(a) Find a 95 percent confidence interval for the population mean concentration of uric acid in this patient's blood. What is the margin of error?

(b) What conditions are necessary for your calculations?

(c) Give a short interpretation of your results in the context of this problem.

(d) Find the sample size necessary for a 95 percent confidence level with maximal error of estimate E = 1.10 for the mean concentration of uric acid in this patient's blood.