A doctor wants to estimate the HDL cholesterol of all 20 to 29 year old females. How many subjects are needed to estimate the HDL cholesterol within 2 points with 99% confidence assuming s-17.8 based on earlier studies. Suppose the doctor would be content with 90 % confidence.
A) A 99% confidence level requires ___ subjects
B) A 90% confidence level re
quires____ subjects?
Answered in a previous post.
To estimate the sample size required to estimate the HDL cholesterol within a certain margin of error and confidence level, we can use the formula for sample size calculation:
n = (Z^2 * s^2) / E^2
Where:
n = required sample size
Z = critical value corresponding to the desired confidence level
s = estimated standard deviation of the population
E = margin of error (half the desired confidence interval width)
Given information:
Confidence level = 99% (for part A) and 90% (for part B)
s = 17.8
E = 2
A) For a 99% confidence level:
First, we need to find the critical value (Z) using a standard normal distribution table or a calculator.
For a 99% confidence level, the critical value is approximately 2.576.
Using the formula:
n = (Z^2 * s^2) / E^2
n = (2.576^2 * 17.8^2) / 2^2
n = (6.650176 * 317.84) / 4
n = 2104.3805 / 4
n ≈ 526.095
Therefore, a 99% confidence level requires approximately 527 subjects.
B) For a 90% confidence level:
Using the same formula and substituting the corresponding critical value:
For a 90% confidence level, the critical value is approximately 1.645.
n = (Z^2 * s^2) / E^2
n = (1.645^2 * 17.8^2) / 2^2
n = (2.7004025 * 317.84) / 4
n = 857.5337 / 4
n ≈ 214.384
Therefore, a 90% confidence level requires approximately 215 subjects.