A doctor want to estimate the HDL cholesterol of all 20- to 29- year old females. how many subjects are needed to estimate the HDL cholesterol within 3 points with 99% confindence assuming s=15.8 based on earlier studies?

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (.005) and its Z score.

3 = Z (s/√n) = 2.575 (15.8/√n)

Solve for n.

To estimate the required sample size, we can use the formula for estimating sample size for a mean:

n = (Z * σ / E)^2

where:
n = required sample size
Z = Z-value for the desired confidence level (99% confidence corresponds to a Z-value of 2.576)
σ = population standard deviation
E = maximum error tolerance (3 points)

Given:
Z = 2.576
σ = 15.8
E = 3

Substituting these values into the formula, we get:

n = (2.576 * 15.8 / 3)^2

Simplifying further:

n = (40.7568 / 3)^2
n = 13.5856^2
n ≈ 184.63

Therefore, we need approximately 185 subjects to estimate the HDL cholesterol within 3 points with 99% confidence, assuming a population standard deviation of 15.8 based on earlier studies. Since you cannot have a fraction of a subject, you would round up to the nearest whole number, so the final answer would be a sample size of 186 subjects.