Question

At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.026 for the estimation of a population proportion? Assume that past data are not available for developing a planning value for p*. Round up to the next whole number.

Answer 1

Solution:

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.026

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

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

= (1.960 / 0.026)² * 0.5 * 0.5

= 1420.62

= 1421

n = sample size = 1421