A doctor wants to estimate the HDL cholesterol of all 20- to 29-year-old females

Question

A doctor wants to estimate the HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the HDL cholesterol within 3 points with 99% confidence assuming =19.5? Suppose the doctor would be content with 95% confidence. How does the decrease in confidence affect the sample size required?

A 99% confidence level requires___subjects. (Round up to the nearest whole number as needed.)

A 95% confidence level requires ___ subjects. (Round up to the nearest whole number as needed.)

How does the decrease in confidence affect the sample size required?

A. The sample size is the same for all levels of confidence.

B. The lower the confidence level the larger the sample size.

C. The lower the confidence level the smaller the sample size.

Explanation / Answer

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) = 19.5
ME =3
n = ( 2.58*19.5/3) ^2
= (50.31/3 ) ^2
= 281.23 ~ 282      
b.
Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.05% LOS is = 1.96 ( From Standard Normal Table )
Standard Deviation ( S.D) = 19.5
ME =3
n = ( 1.96*19.5/3) ^2
= (38.22/3 ) ^2
= 162.31 ~ 163      
c.
C. The lower the confidence level the smaller the sample size.

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