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 ? = 1.85 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.)
? is unknownuniform distribution of uric acidn is large? is knownnormal distribution of uric acid
(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 0.05.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 not enough information to make an interpretation.There is a 95% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient.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 = 1.08 for the mean
concentration of uric acid in this patient's blood. (Round your
answer up to the nearest whole number.)
blood tests
Solution:
a) 95%CI = mean +/- 1.96*sigma/sqrt(n)
= 5.35 +/- 1.96*1.85/sqrt(11)
= 5.35+/- 1.09 = (4.26, 6.44)
b) normal distribution of uric acid
sigma is known
c) Without looking at the choices, this means that the true value for the patient is highly likely to be in this interval. The true value, of course, is either in the interval or isn't, which is a 0-100% probability question, not helpful. One can be highly confident, however, that the true value is in this interval.
Stated another way, if there were 100 CIs constructed, 95 of
them would contain the true value. We just don't know which 95 of
them.
d) With the choices above, the second from the bottom "There is a
95% chance that..." would be the answer.
For the sample size, 1.96*1.85/sqrt(n) <=1.08
=>1.08* sqrt(n)>=3.626
=> sqrt (n) >= 3.357
=> n >= 11.269 or 12
Get Answers For Free
Most questions answered within 1 hours.