Question

A doctor wants to estimate the HDL cholesterol of all​ 20- to​ 29-year-old females. How many subjects are needed to estimate the HDL cholesterol within 22 points with 99% confidence assuming sigma equals 15.2 question mark σ=15.2? Suppose the doctor would be content with 90% confidence. How does the decrease in confidence affect the sample size​ required?

A​ 99% confidence level requires

A 90% confidence level require

Answer 1

Solution :

Given that,

Population standard deviation = = 15.2

Margin of error = E = 2

(a) 99%

Z_/2 = 2.576

sample size = n = [Z_/2* / E] ²

n = [2.576 * 15.2/ 2]²

n = 384

A​ 99% confidence level requires 384

(b) 90%

Z_/2 = 1.645

sample size = n = [Z_/2* / E] ²

n = [1.645 * 15.2/ 2]²

n = 157

A​ 90% confidence level requires 157