Question

A California animal shelter is interested in studying the rate of animals that get surrendered to shelters by their owners. What sample size is needed to estimate this proportion with a 95% confidence interval and a 3% margin of error? Round up.

Answer 1

Solution:

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 3% = 0.03

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.960

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

= (1.960 / 0.03)2 * 0.5 * 0.5

= 1067

n = sample size = 1067