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 33 points with 99 %99% confidence assuming s equals 16.6s=16.6 based on earlier​ studies? Suppose the doctor would be content with 90 %90% confidence. How does the decrease in confidence affect the sample size​ required?

Answer 1

a.
AT 99%
Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Zα/2 at 0.01% LOS is = 2.58 ( From Standard Normal Table )
Standard Deviation ( S.D) = 16.6
ME =3
n = ( 2.58*16.6/3) ^2
= (31.48/2 ) ^2
= 203.80~ 204

AT 95%
Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Zα/2 at 0.05% LOS is = 1.96 ( From Standard Normal Table )
Standard Deviation ( S.D) = 16.6
ME =3
n = ( 1.96*16.6/3) ^2
= (10.8453333 ) ^2
= 117.62~ 118

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