Question

Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advanced indication of illness such as gout leukemia or lymphoma. Over a period of months an adult Male patient has taken eight blood tests for uric acid. The sample mean concentration was 5.33 mg/dL . The distribution of uric acid in healthy adult Males can be assumed to be normal, with population standard deviation 1.85 mg/dL. In steps we are going to find a 95% confidence interval for the population mean.

1a. In order to find any confidence interval in the chapter, you must calculate the EBM ( error bound) value. In this case you must identify the critical value to be used for zCL.

b. What is the error bound for a population mean, EMB, for this problem.

c. What is the range from low to high for the population mean.

d. Interpret the confidence interval in the context of the problem.
I am 95% confident that.............

2. What is the critical value for a 99% confidence level when the sample size is 14 and s is known?

b. What is the critical value of 95% confidence level when the sample size is 44 and s is known?

Answer 1

a) At 95% confidence level, the critical value is z_{0.025 =} 1.96

b) Margin of error = z_0.025 *

                         = 1.96 * 1.85/

                         = 1.282

c) The 95% confidence interval is

+/- E

= 5.33 +/- 1.282

= 4.048, 6.612

d) I am 95% confident that the true mean concentration of uric acid lies in the above confidence interval.

2) a) At 99% confidence level, the critical value is z_{0.005 =} 2.58

Since is known and the population is normally distributed, so we will use z-critical value.

b) At 95% confidence level, the critical value is z_{0.025 =} 1.96

Since is known and the population is normally distributed, so we will use z-critical value.