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 subject are needed to estimate the mean HDL cholesterol within 2 point with 99% confidence assuming = 10.9 based on earlier studies? Suppose the doctor would be content with 95% confidence. How dose the decrease in confidence affect the sample size required? A 99% confidence level required subjects. (Round up to the nearest subject.) A 95% confidence level required subject. (Round up to the nearest subject.) How dose 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.

Explanation / Answer

Sample size (n) = (s * zc )^2 / E^2

For 99% confidence interval we get the critical z value as 2.576 from normal table.

s = 10.9

E = 2

Sample size (n) = (10.9 * 2.576 )^2 / 2^2

                            = 197.10

                           ~ 197

Answer:

A 99% confidence level requires 197 subjects.

For 95% confidence interval we get the critical z value as 1.96 from normal table.

s = 10.9

E = 2

Sample size (n) = (10.9 * 1.96 )^2 / 2^2

                            = 114.11

                           ~ 114

Answer:

A 95% confidence level requires 114 subjects.

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

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