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=16.2 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,

1)

Population standard deviation = = 16.2

Margin of error = E = 4

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* / E) 2

n = (2.576 * 16.2/ 4)2

n = 108.84

n = 109

Sample size = 109

2)

Population standard deviation = = 16.2

Margin of error = E = 4

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

sample size = n = (Z/2* / E) 2

n = (1.96 * 16.2/ 4)2

n = 63.01

n = 64

Sample size = 64