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 15.6 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 = 15.6

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 = Z_0.005 = 2.576

Sample size = n = ((Z_/2 * s) / E)²

= ((2.576 * 15.6) /4)²

= 100.93 = 101

Sample size = 101

If we decrease the confidence level the sample size is decreased .