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 equals 12.4 based on earlier​ studies? Suppose the doctor would be content with 95 % confidence. How does the decrease in confidence affect the sample size​ required? LOADING... Click the icon to view a partial table of critical values. A​ 99% confidence level requires 64 subjects. ​(Round up to the nearest​ subject.) A 95 % confidence level requires 37 subjects. ​(Round up to the nearest​ subject.) How does the decrease in confidence affect the sample size​ required? A. The sample size is the same for all levels of confidence. B. Decreasing the confidence level increases the sample size needed. C. Decreasing the confidence level decreases the sample size needed.

Answer 1

for 99% CI

for 99 % CI value of z=	2.576
standard deviation σ=	12.40
margin of error E =	3
required sample size n=(zσ/E)2                                         =	114.0

for 95% CI:

for 95 % CI value of z=	1.960
standard deviation σ=	12.40
margin of error E =	3
required sample size n=(zσ/E)2                                         =	66.0

from above:

A​ 99% confidence level requires 114 subjects

A 95 % confidence level requires 66 subjects.

C. Decreasing the confidence level decreases the sample size needed.