Question

We would like to estimate the average age in the population. Assume that standard deviation is equal to 10 years. Compute the optimal sample size in case of maximum tolerable error of 2 units and significance level 0,05. Population size is not known.

Answer 1

Solution:
Given in the question
Population standard deviation () = 10
Maximum tolerable error or Margin of error (E) = 2
Here level of significance or = 0.05
/2 = 0.025
From Z table we found Z/2 = 1.96
So Sample size n can be calculated as
Sample size (n) = (Z/2 * /E)^2 = (1.96*10/2)^2 = (9.8)^2 = 96.04 or 96
So sample size required = 97
the optimal sample size in case of maximum tolerable error of 2 units is 96.