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

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 2 points with 99% confidence assuming s=11.7 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?

A) Decreasing the confidence level increases the sample size needed.

B) The Sample size is the same for all levels of confidence.

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

Explanation / Answer

Required ME = 2
s = 11.7

ME = z * s/sqrt(n)
n = (z * s / ME)^2

For 99% CI, z = 2.58
n = (2.58*11.7/2)^2 = 227.7986 i.e. 228

For 90% CI, z = 1.65
n = (1.65*11.7/2)^2 = 93.1707 i.e. 93

Decreasing the confidence level increases the sample size needed.

Option (A)

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