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 3 points with 99% confidence assuming s=12.5 based on earlier​ studies? Suppose the doctor would be content with 90% confidence. How does the decrease in confidence affect the sample size​ required?

Answer 1

for 99% confidence interval:

for 99 % CI value of z=	2.576
standard deviation σ=	12.50
margin of error E =	3
required sample size n=(zσ/E)2                                         =	116.0

for 90% confidence interval:

for 90 % CI value of z=	1.645
standard deviation σ=	12.50
margin of error E =	3
required sample size n=(zσ/E)2                                         =	47.0

hence decreasing  confidence interval to 90% will decrease the requirement of sample size.