A doctor wants to estimate the mean HDL cholesterol of all 2

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 = 12.6 based on earlier studies? Suppose the doctor would be content with 90% confidence. How does the decrease in confidence affect the sample size required? A 99% confidence level requires subjects. (Round up to the nearest subject.) A 90% confidence level requires subjects. (Round up to the nearest subject.) How does the decrease in confidence affect the sample size required?

Solution

a)
Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.01% LOS is = 2.58 ( From Standard Normal Table )
Standard Deviation ( S.D) = 12.6
ME =2
n = ( 2.58*12.6/2) ^2
= (32.508/2 ) ^2
= 264.193 ~ 265      
b)
Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.1% LOS is = 1.64 ( From Standard Normal Table )
Standard Deviation ( S.D) = 12.6
ME =2
n = ( 1.64*12.6/2) ^2
= (20.664/2 ) ^2
= 106.75 ~ 107      

c)
DEcreasing the Confidence level decreases the sample size needed