(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:
[tex]n = [\frac{z X s}{E}]^2[/tex]
On substituting the value, we get:
[tex]n = [\frac{2.576 X 15.6}{2} ]^2\\\\n = 403.7[/tex]
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:
[tex]n = [\frac{z X s}{E}]^2[/tex]
On substituting the value, we get:
[tex]n = [\frac{1.96 X 15.6}{2} ]^2\\\\n = 233.7[/tex]
n = 234
Thus, when the confidence level decreases to 95%, the number of subjects decreases from 404 to 234.
