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?
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 = Z0.025 = 1.96
sample size = n = [Z/2* / E] 2
n = ( 1.96*0.2 /0.1 )2
n =15.3664
Sample size = n =16
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