Question

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 3 points with 99 % confidence assuming sigma equals 15.7 question mark Suppose the doctor would be content with 90 % confidence. How does the decrease in confidence affect the sample size? required?

Answer 1

a) We are given the margin of error here as: MOE = 3

From standard normal tables, we have:
P( -2.576 < Z < 2.576) = 0.99

The margin of error is computed as:

Therefore 182 is the sample size required here.

b) For 90% confidence interval, we have from the standard normal tables,
P(-1.645 < Z < 1.645 ) = 0.9

Therefore the sample size required here is:

Therefore 75 is the minimum sample size required here.

Clearly as the confidence interval decreases, the sample size required decreases too for the same margin of error.