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 33 points with 99 %99% confidence assuming s equals 11.2s=11.2 based on earlier​ studies? Suppose the doctor would be content with 95 %95% confidence. How does the decrease in confidence affect the sample size​ required? A​ 99% confidence level requires ____subjects. A​ 95% confidence level requires ____subjects.

Answer 1

Solution:- Given that s = 11.2, E = 3

95% confidence interval
The critical value corresponding to the given situation is obtained as Z(α/2) = 1.96
1 - α = 1 - 0.95
α = 0.05
α/2 = 0.05/2 = 0.025
Z0.05 = 1.96

99% confidence interval
The critical value corresponding to the given situation is obtained as Z(α/2) = 2.576
1 - α = 1 - 0.99
α = 0.01
α/2 = 0.01/2 = 0.005
Z0.005 = 2.576

A 99% confidence level requires 93 subjects

n = (Z*S/E)^2 = (2.576*11.2/3)^2 = 92.487 = 93

A 95% confidence level requires 54 subjects

n = (Z*S/E)^2 = (1.96*11.2/3)^2 = 53.543 = 54