Question

A test for the level of potassium in the blood is not perfectly precise.  Moreover, the actual level of potassium in a person's blood varies slightly from day to day. Suppose that repeated measurements for the same person on different days vary Normally with a standard deviation of 0.2 mg/dl.

Suppose Julie's doctor would like a very precise estimate of her potassium level. At a 95% confidence level, how many days will the doctor need to take samples to have a margin of error less that 0.1 mg/dl?

Answer 1

Solution

standard deviation =   =0.2

Margin of error = E = 0.1

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

sample size = n = [Z_/2* / E] ²

n = ( 1.96* 0.2 / 0.1 )²

n =15.36

Sample size = n =16