Question

We are interested in conducting a study in order to determine what percentage of voters would vote for the incumbent president. What is the minimum size sample needed to estimate the population proportion with a margin of error of 0.01 or less at 90% confidence?

Answer 1

Solution,

Given that,

=  1 - = 0.5

margin of error = E = 0.01

At 90% confidence level

= 1 - 90%

= 1 - 0.90 =0.10

/2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= (1.645 / 0.01)² * 0.5 * 0.5

= 6765.06

sample size = n = 6766