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 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 = 1.95 mg/dl.

(a) 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.)

lower limit
upper limit
margin of error

(d) Find the sample size necessary for a 95% confidence level with maximal margin of error E = 1.00 for the mean concentration of uric acid in this patient's blood. (Round your answer up to the nearest whole number.)

Answer 1

Solution :

Given that,

(a)

Z_/2 = 1.96

Margin of error = E = Z_/2* ( /n)

= 1.96 * (1.95 / 8)

= 1.35

At 95% confidence interval estimate of the population mean is,

- E < < + E

5.35 - 1.35 < < 5.35 + 1.35

4.00 < < 6.70

Lower limit = 4.00

Upper limit = 6.70

Margin of error = 1.35

(b)

Z_/2 = 1.96

sample size = n = [Z_/2* / E] ²

n = [1.96 * 1.95 / 1]²

n = 15

Sample size = n = 15