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=14.3 based on earlier​ studies? Suppose the doctor would be content with 95% confidence. How does the decrease in confidence affect the sample size​ required?

Answer 1

Solution :

Given that,

standard deviation = S = 14.3

margin of error = E = 4

a ) At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576

Sample size = n = ((Z/2 * S) / E)2

= ((2.576 * 14.3 ) / 4 )2

= 85

Sample size = 85

b ) At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.960

Sample size = n = ((Z/2 * S) / E)2

= ((1.960 * 14.3 ) / 4 )2

= 49

Sample size = 49

c ) The decrease in confidence level decrease in sample size.