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

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 = 14.4 based on earlier studies?  Suppose the doctor would be content with 90% confidence.  How does the decrease in confidence affect the sample size?

A 99% confidence level requires _ subjects. (round to the nearest subject)

A 90% confidence level requires _ subjects. (round to the nearest subject)

How does the decrease in confidence affect the sample size required? (choose)

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.

Explanation / Answer

For 99% confidence interval the critical value is z0.005 = 2.58
margin of error = 3

or, z0.005 * sd/sqrt(n) = 3

or, 2.58 * 14.4/sqrt(n) = 3

or, sqrt(n) = 2.58 * 14.4/3

or, sqrt(n) = 12.384

or, n = 153

For 90% confidence interval the critical value is z0,05 = 1.645

margin of error = 3

or, z0.05 * sd/sqrt(n) = 3

or, 1.645 * 14.4/sqrt(n) = 3

or, sqrt(n) = 1.645 * 14.4/3

or, sqrt(n) = 8

or, n = 64

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

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