Question

Patient has taken fifteen blood tests for uric acid. The mean concentration was x 5.44 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with it-1.93 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.)
Tower mit
upper limit
margin of error
(b) What conditions are necessary for your calculations? (Select all that apply)
On is large
Duniform distribution of uric acid
normal distribution of uric acid
is known
De is unknown
(e) Interpret your results in the context of this problem.
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 0.05.
The probability that this interval contains the true average unic acid level for this patient is 0.05.
We are 5% confident that the true uric acid level for this patient falls within this interval
(0) Find the sample size necessary for a 95% confidence level with maximal margin of error -1.14 for the mean concentration of uric acid in this patient's blood.

Answer 1

The 95% confidence interval for the uric acid concentration in the patient's blood is approximately (4.84, 6.04) mg/dl with a margin of error of 0.97. The necessary conditions for this calculation are a normal distribution of uric acid and a known standard deviation. We are 95% confident that this patient's true uric acid level falls within this range.

Step-by-step explanation:

To find a 95% confidence interval for the population mean concentration of uric acid in the patient's blood, you would use the formula for a confidence interval when the standard deviation (σ) is known:

(μ - Z* σ / √ n , μ + Z* σ / √ n)

Where μ is the sample mean, σ the standard deviation of the population, n is the sample size, and Z is the Z-value corresponding to the desired confidence level. Here we assume that the sample mean (μ) is 5.44 mg/dl, σ is 1.93 mg/dl, and n is 15. The Z-value for a 95% confidence level is approximately 1.96.

The calculated confidence interval is (5.44 - (1.96*1.93/√15), 5.44 + (1.96*1.93/√15)). After computing, we get approximately (4.84, 6.04) and the margin of error would be the distance from the sample mean to one of the bounds, which is 1.96*1.93/√15, approximately 0.97.

For part (b), the conditions necessary for these calculations are:

σ is known

The correct interpretation of the confidence interval result (part c) is:

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

For the sample size necessary for a 95% confidence level (part d) with a maximal margin of error of -1.14, we would adjust the margin of error in the original formula to solve for n:

n = (Z*σ/EBM)^2

The value of n must be rounded up to the nearest whole number once calculated. The comprehensive answer would include this calculation.