Question

If you want to be 95%confident of estimating the population proportion to within a sampling error plus or minus ± 0.05 and there is historical evidence that the population proportion is approximately    0.38

what sample size is​ needed?

Answer 1

Solution :

Given that,

= 0.38

1 - = 1 - 0.38 = 0.62

margin of error = E = 0.05

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = 1.96

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

= (1.96 / 0.05)² * 0.38 * 0.62

= 362.03

sample size = n = 363