Question

1. Suppose you want to estimate the proportion of students on your campus who own their own car. You have no preconceived idea of what that proportion might be.

What sample size needed if you wish to be 95% confident that your estimate is within o.o2 of the true proportion?

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5= 0.5

margin of error = E = 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 ( Using z table  

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

= (1.96 / 0.02)2 * 0.5 * 0.5

= 2401

Sample size = 2401