) Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of an illness such as gout, leukemia, or lymphoma. Over a period of months, an adult male patient has taken eight blood tests for uric acid. His mean concentration was mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with ó = 1.85. You are interested in a 99% confidence interval for the mean concentration of uric acid for this patient.

___(a) Write down the proper formula to use
________________________________(b) What is the value of or for your interval
_____________________________ (c) What is the value of the margin of error for your interval
__________________________________________ (d) Give the 99% confidence interva
(e) Interpret your interval in the context of the problem.
_______________________ (f) How many blood tests would you need to take to have 99% confidence and have a margin of error of only E = 1.25

Formula:

CI99 = mean + or - 2.58(sd/√n)

...where + or - 2.58 represents the 99% confidence interval using a z-table; sd = standard deviation; n = sample size.

I'll let you take it from here.

(a) The formula to use in this case is the confidence interval formula for a population mean:

Confidence Interval = sample mean ± (critical value * standard deviation / square root of sample size)

(b) To find the critical value, we need to look up the value from the standard normal distribution table. For a 99% confidence level, we need to locate the value that corresponds to a tail probability of (1 - 0.99) / 2 = 0.005. The z-value for this tail probability is approximately 2.58.

(c) The margin of error is calculated by multiplying the critical value by the standard deviation divided by the square root of the sample size:

Margin of Error = 2.58 * (standard deviation / square root of sample size)

(d) The 99% confidence interval can be calculated by subtracting and adding the margin of error to the sample mean:

99% Confidence Interval = sample mean - margin of error, sample mean + margin of error

(e) The 99% confidence interval represents a range of values within which we can be 99% confident that the true population mean concentration of uric acid for this patient lies. In other words, if we were to take multiple samples from this patient and calculate confidence intervals using the same method, approximately 99% of these intervals would contain the true population mean.

(f) To determine the number of blood tests needed to achieve a 99% confidence level and a margin of error of 1.25, we can rearrange the margin of error formula:

n = (Z^2 * σ^2) / E^2,

where n is the required sample size, Z is the critical value, σ is the standard deviation, and E is the desired margin of error.

Plugging in the values, we get:

n = (2.58^2 * σ^2) / 1.25^2.