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 3 points with 99 % confidence assuming s equals 16.9 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 ,

= 16.9 ..Population SD

(taking s as an estimate of the )

E = 3 Margin of error

c = 99% = 0.99 ...confidence level

c = 0.99

= 1- c = 1- 0.99 = 0.01

  /2 = 0.005

Using Z table ,

= 2.576

Now, sample size (n) is given by,

=  {(2.576 * 16.9)/ 3}²

= 210.58

= 211 ..(round to the next whole number)

Answer: For 99% confidence , required sample size is n = 211

Now suppose that we use 95% confidence level instead of 99%

c = 95% = 095

= 1- c = 1- 0.95 = 0.05

  /2 = 0.025

Using Z table ,

= 1.96

As confidence level decreases , decreases.

Observe the formula for n.

n is directly proportional to

So ,

As confidence level decreases , n also decreases.