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 3 points with 99% confidence assuming s= 11.9 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 95 % 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 level affect the sample size? Decreasing the confidence level decreases the sample size. Decreasing the confidence level increases the sample size. The sample size is the same for all levels of confidence.

Explanation / Answer

1) 99%confidence interval requires 105 subjects approximately

99%cofidence of z value is 2.5758

S=11.9,E=3
n = [zs/E]^2
n = [2.5758*11.9/3]^2

n=104.394( 105 subjects)

2) 9 5%confidence interval requires 61 subjects approximately

95%cofidence of z value is 1.96

S=11.9,E=3
n = [zs/E]^2
n = [1.96*11.9/3]^2

n=60.5(61 subjects are required)

3) 90% confidential interval requires 43 subjectS

99%cofidence of z value is 1.65

S=11.9,E=3
n = [zs/E]^2
n = [1.65*11.9/3]^2

n=42.8(43 subject s are required)

Above three cases we can find that "decreasing the confidential interval decreases sample size."

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