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 4 points with 99 % confidence assuming s equals 10.9 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. A 99% confidence level requires __ subjects.

B. A 95% confidence level requires __ subjects.

Answer 1

Solution :

Given that,

Population standard deviation = = 10.9

Margin of error = E = 4

a) At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005 = 2.576

  sample size = n = [Z/2* / E] 2

n = [2.576 * 10.9 / 4]2

n = 49.27

Sample size = n = 50

b) At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96

  sample size = n = [Z/2* / E] 2

n = [1.96 * 10.9 / 4]2

n = 28.53

Sample size = n = 29