Question

What is the minimum sample size needed to estimate the mean age of the books in a library to within 2 months with 95% confidence if the standard deviation of the ages is thought to be about 60 months?

Answer 1

Solution :

Given that,

standard deviation = = 60

margin of error = E = 2

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 = 1.960

Sample size = n = ((Z_/2 * ) / E)²

= (1.960 * 60) / 2)²

=3457.44

= 3457

The minimum sample size = 3457