Question

Find the minimum sample size n necessary to estimate a population proportion p with a 95% confidence interval that has a margin of error m = 0.04. Assume that you don’t have any idea what p is so that you use the simpler formula for n (which comes from taking the more complicated formula for n and substituting p∗ = 0.5 into it).

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.04

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 ( Using z table )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.96 / 0.04)2 * 0.5 * 0.5

= 600.25

Sample size =600 ROUNDED

some time answer came 601