(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.
Step-by-step 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 = [(z X s)/(E)]^2](https://img.qammunity.org/2021/formulas/mathematics/high-school/vy84977xpfsn912jd2bkcc0tb0vdpppboo.png)
On substituting the value, we get:
![n = [(2.576 X 15.6)/(2) ]^2\\\\n = 403.7](https://img.qammunity.org/2021/formulas/mathematics/high-school/5a1jqt0qudmdsq95vykidl57tiuxrapq8o.png)
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 = [(z X s)/(E)]^2](https://img.qammunity.org/2021/formulas/mathematics/high-school/vy84977xpfsn912jd2bkcc0tb0vdpppboo.png)
On substituting the value, we get:
![n = [(1.96 X 15.6)/(2) ]^2\\\\n = 233.7](https://img.qammunity.org/2021/formulas/mathematics/high-school/wdvi4cu6rfi4g5ldxezffmq27wo1e20k30.png)
n = 234
Thus, when the confidence level decreases to 95%, the number of subjects decreases from 404 to 234.