Question

A doctor wants to estimate the mean HDL cholesterol of all​ 20- to​ 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 2 points with 99 % confidence assuming s equals 15.6 based on earlier​ studies? Suppose the doctor would be content with 95 % confidence. How does the decrease in confidence affect the sample size​ required?

Answer 1

(a) 404 subjects are needed to estimate the mean HDL cholesterol within 2 points with 99% confidence.

(b) When the confidence level decreases to 95%, the number of subjects decreases from 404 to 234.

Explanation:

Given:

σ = 15.6

Let the number of subjects be n

(a)

When the confidence level is 99%, then z = 2.576

E = 2

We know:

$n = [\frac{z X s}{E}]^2$

On substituting the value, we get:

$n = [\frac{2.576 X 15.6}{2} ]^2\\\\n = 403.7$

Thus, 404 subjects are needed to estimate the mean HDL cholesterol within 2 points with 99% confidence.

(b)

When the confidence level is 95%, then z = 1.96

E = 2

We know:

$n = [\frac{z X s}{E}]^2$

On substituting the value, we get:

$n = [\frac{1.96 X 15.6}{2} ]^2\\\\n = 233.7$

n = 234

Thus, when the confidence level decreases to 95%, the number of subjects decreases from 404 to 234.