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 = 11.3 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 A 90% confidence level requires How does the decrease in confidence affect the sample size required? Decreasing the confidence level increases the sample size needed. The sample size is the same for all levels of confidence. Decreasing the confidence level decreases the sample size needed.

Explanation / Answer

THE MARGIN OF ERROR = 2

THE FORMULA FOR MARGIN OF ERROR = ZSCORE*STANDARD DEVIATION/SQRT(N)

A) THEREFORE ACCORDING TO FORMULA

Z SCORE FOR 99% = 2.57

2 = 2.57*11.3/SQRT(N)

SQUARING BOTH SIDES

N = (2.57*11.3/2)^2

= 211

B) Z SCORE FOR 90% = 1.645

THEREFORE

2 = 1.645*11.3/SQRT(N)

SQUARING BOTH SIDES

N = (1.645*11.3/2)^2

= 86

C) DECREASE IN CONFIDENCE INTERVAL DECREASES THE SIZE OF THE SAMPLE

THEREFORE OPTION C IS CORRECT

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