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 twelve 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 = 1.87 mg/dl.

(a) Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. (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.)

uniform distribution of uric acidn is largenormal distribution of uric acidσ is knownσ is unknown

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

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

(d) Find the sample size necessary for a 95% confidence level with maximal error of estimate E = 1.08 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

Solution :

Given that,

Point estimate = sample mean = = 5.35

Population standard deviation =    = 1.87

Sample size = n = 12

a) At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_0.025 = 1.96

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

E = 1.96 * (1.87 /  12 )

E = 1.06

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

  ± E

5.35 ± 1.06

( 4.29, 6.41)  

lower limit = 4.29

upper limit = 6.41

margin of error = 1.06

b) σ is known

normal distribution of uric acid

c) There is a 95% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient

d) margin of error = E = 1.08

sample size = n = [Z_/2* / E] ²

n = [1.96 *1.87 / 1.08]²

n = 11.51

Sample size = n = 12 blood tests