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=17.8

based on earlier​ studies? Suppose the doctor would be content with

95%

confidence. How does the decrease in confidence affect the sample size​ required?

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A​ 99% confidence level requires

nothing

subjects. ​(Round up to the nearest​ subject.)A

95 %95%

confidence level requires

nothing

subjects. ​(Round up to the nearest​ subject.)

How does 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 decreases the sample size needed.

C.

Decreasing the confidence level increases the sample size needed.

Answer 1

Solution :

a) Z/2 = Z0.005 = 2.576  

sample size = n = [Z/2* / E] 2

n = [2.576 * 17.8 / 2]2

n = 525.61

Sample size = n = 526 subjects.

Z/2 = Z0.025 = 1.96

sample size = n = [Z/2* / E] 2

n = [1.96 * 17.8 / 2]2

n = 304.29

Sample size = n = 305 subjects.

c) B. Decreasing the confidence level decreases the sample size needed.