Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. What is the margin of error? (Round your answers to two decimal places.

Question

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 ten 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 = 1.91 mg/dl.

 

Answer 1

The small sample size of 10 suggests using a t-test with 9 degrees of freedom and a 95% 2-tailed confidence level. From t-tables we get t=2.262. We need to adjust the pop SD to 1.91/√10=0.604.

X represents a value above the mean such that (X-5.35)/0.604=2.262, X-5.35=1.37 approx. So 3.98≤X≤6.72 mg/dl. With 95% confidence the mean will be in this range.