Question

The dwarves of the Grey Mountains wish to conduct a survey of their pick-axes in order to construct a 95% confidence interval about the proportion of pick-axes in need of repair. What minimum sample size would be necessary in order ensure a margin of error of 2 percentage points (or less) if they do not have a prior estimate of the percentage of pick-axes that are in need of repair?

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 2% = 0.02

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 * * (1 - )

= (1.96 / 0.02)2 * 0.5 * 0.5

= 2401

Sample size =2401