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

(b) What conditions are necessary for your calculations? (Select all that apply.)

σ is unknownuniform distribution of uric acidn is largenormal distribution of uric acidσ is known

(c) Interpret your results in the context of this problem.

The probability that this interval contains the true average uric acid level for this patient is 0.95.The probability that this interval contains the true average uric acid level for this patient is 0.05.     There is a 5% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient.There is a 95% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient.There is not enough information to make an interpretation.

(d) Find the sample size necessary for a 95% confidence level with maximal margin of error E = 1.06 for the mean concentration of uric acid in this patient's blood. (Round your answer up to the nearest whole number.)
blood tests

Answer 1

a)

CI for 95%

n = 8

mean = 5.35

t-value of 95% CI = 2.3646

std. dev. = 1.9500

SE = std.dev./sqrt(n) = 1.95/sqrt(8) = 0.68943

Margin of error, ME = t*SE = 2.3646*0.68943 = 1.63024

Lower Limit = Mean - ME = 5.35 - 1.63024 = 3.71976

Upper Limit = Mean + ME = 5.35 - 1.63024 = 6.98024

95% CI (3.7198 , 6.9802 )

b)

normal distribution

sigma is known

c)

The probability that this interval contains the true average uric acid level for this patient is 0.95.

d)

Given CI Level 95%

Margin of Error(ME) = 1.06

std. dev. = 1.95

z-value of 95% CI = 1.9600

n = (z*sigma/ME)^2

=(1.96*1.95/1.06)^2

= 13