Question

9.2.41 10 8 based on earlier 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 studies? Suppose the doctor would be content with 95% confidence How does the decrease in confidence affect the sample size required? cholesterol within 2 points with 99% confidence assuming s Click the icon to view a partal table of critical values Partal Critical Value Table A 99% confidence level requires subjects (Round up to the nearest subject ) Critical Value, za /2 Level of Confidence, (1-a). 100%ce, Area in Each Tail,or 1 645 90% 95% 0051 0025 0 005 2 575 Print Done

Answer 1

i) With 99% confidence level,

To find n such that

Margin of error = 2

$\Rightarrow z_{0.005}*\frac{s}{\sqrt{n}} = 2$

$\Rightarrow 2.575*\frac{10.8}{\sqrt{n}} = 2$

$\Rightarrow \sqrt{n}=\frac{2.575*10.8}{2}$

$\Rightarrow n=(\frac{2.575*10.8}{2})^2 = 13.905^2 = 193.349 \approx 194$

$\Rightarrow n \approx 194$

ii) With 95% confidence level,

To find n such that

Margin of error = 2

$\Rightarrow z_{0.025}*\frac{s}{\sqrt{n}} = 2$

$\Rightarrow 1.96*\frac{10.8}{\sqrt{n}} = 2$

$\Rightarrow \sqrt{n}=\frac{1.96*10.8}{2}$

$\Rightarrow n=(\frac{1.96*10.8}{2})^2 = 10.5840^2 = 112.021 \approx 112$

$\Rightarrow n \approx 112$

Decrease in confidence reduces the required sample size.