Question

A 99% confidence interval has to be created to estimate the mean of the volume of contents in the bottles of an expensive medication. How large a simple random sample has to be taken so that the margin of error is no more than ±5 ml? Assume that the population standard deviation is 20 ml.

Answer 1

Solution :

Given that,

Population standard deviation = = 20 ml.

Margin of error = E = 5 ml.

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2  = 0.005

Z_/2 = 2.576

sample size = n = [Z_/2* / E] ²

n = [ 2.576 * 20 / 5 ]²

n = 106.17

Sample size = n = 107