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 22 points with 99% confidence assuming s equals 11.9 based on earlier​ studies? Suppose the doctor would be content with 95% confidence. How does the decrease in confidence affect the sample size required?

A 99% confidence level requires ? subjects (please answer the question mark for both)

A 95% confidence level requires ? subjects

Answer 1

Solution :

Given that margin of error E = 22 , standard deviation s = 11.9

=> For 99% confidence level , Z = 2.58

=> Sample size n = (Z*s/E)^2

= (2.58*11.9/22)^2

= 1.9475

= 2 (nearest whole number)

=> For 95% confidence level , Z = 1.96

=> Sample size n = (Z*s/E)^2

= (1.96*11.9/22)^2

= 1.1240

= 1 (nearest whole number)

==> A 99% confidence level requires 2 subjects

==> A 95% confidence level requires 1 subject

=> decreases the confidence level decreases the sample size needed