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=13.3 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 __ subjects? (round up to the nearest subject)

A 90% confidence level requires __ subjects? (round up the the nerest subject)

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

Answer 1

Solution :

a) Z/2 = Z0.005 = 2.576

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

n = [2.576 * 13.3/ 3]2

n = 130.42

Sample size = n = 131

b) Z/2 = Z0.05 = 1.645

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

n = [1.645 * 13.3/ 3]2

n = 53.18

Sample size = n = 54

c) confidence of level is decreases, sample size is decreases