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 = 1.75 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.)

uniform distribution of uric acid n is large normal distribution of uric acid σ is known σ is unknown

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

We are 5% confident that the true uric acid level for this patient falls within this interval. We are 95% confident that the true uric acid level for this patient falls within this interval.     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.

(d) Find the sample size necessary for a 95% confidence level with maximal margin of error E = 1.12 for the mean concentration of uric acid in this patient's blood. (Round your answer up to the nearest whole number.)
blood testsOverproduction 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 = 1.75 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.)

uniform distribution of uric acid n is large normal distribution of uric acid σ is known σ is unknown

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

We are 5% confident that the true uric acid level for this patient falls within this interval. We are 95% confident that the true uric acid level for this patient falls within this interval.     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.

(d) Find the sample size necessary for a 95% confidence level with maximal margin of error E = 1.12 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

Part a)

Confidence Interval :-
X̅ ± Z( α /2) σ / √ ( n )
Z(α/2) = Z (0.05 /2) = 1.96
5.35 ± Z (0.05/2 ) * 1.75/√(12)
Lower Limit = 5.35 - Z(0.05/2) 1.75/√(12)
Lower Limit = 4.3598
Upper Limit = 5.35 + Z(0.05/2) 1.75/√(12)
Upper Limit = 6.3402
95% Confidence interval is ( 4.36 , 6.34 )

Part b)

normal distribution of uric acid

Part c)

We are 95% confident that the true uric acid level for this patient falls within this interval.

Part d)

  Sample size can be calculated by below formula
n = (( Z(α/2) * σ) / e )^2
n = (( Z(0.05/2) * 1.75 ) / 1.12 )^2
Critical value Z(α/2) = Z(0.05/2) = 1.96
n = (( 1.96 * 1.75 ) / 1.12 )^2
n = 10
Required sample size at 95% confidence is 10.