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 eleven 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 = 1.89 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

b) Find the sample size necessary for a 95% confidence level with maximal margin of error E = 1.14 for the mean concentration of uric acid in this patient's blood. (Round your answer up to the nearest whole number.)
x blood tests

Answer 1

a)

sample mean, xbar = 5.35
sample standard deviation, σ = 1.89
sample size, n = 11

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

CI = (5.35 - 1.96 * 1.89/sqrt(11) , 5.35 + 1.96 * 1.89/sqrt(11))
CI = (4.23 , 6.47)

Lower Limit = 4.23
Upper limit = 6.47

Margin of error = z *(s/sqrt(n))
= 1.96 * 1.89/sqrt(11)
= 1.12

Margin of error = 1.12

b)
E = 1.14
z value at 95% = 1.96

ME = z *(s/qrt(n))
1.14 = 1.96 *(1.89/sqrt(n))

n = (1.96 *1.89/1.14)^2

n = 11 blood tests