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 nine 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.)

normal distribution of uric acidn is largeσ is unknownσ is knownuniform distribution of uric acid

(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.The probability that this interval contains the true average uric acid level for this patient is 0.05.     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.

(d) Find the sample size necessary for a 95% confidence level with maximal margin of error E = 1.04 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) The confidence interval for the mean is given by

Here also for 95% confidence interval

So the interval is

b) The conditions that are necessary for calculations, are i) normal distribution of uric acid, ii)  σ is known  

c) Correct Option is

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

d) The margin of error is given by