Question

Assume that the population proportion is .55. Compute the standard error of the proportion, , for sample sizes of 100, 200, 500, and 1000. What can you say about the size of the standard error of the proportion as the sample size is increased?

Answer 1

SE = sqrt [(p)(1-p) / n ]

For n = 100

= sqrt[(0.55)(0.45) / 100 ]

≈ 0.0497

For n = 200

= sqrt[(0.55)(0.45) / 200 ]

≈ 0.0352

For n = 500

= sqrt[(0.55)(0.45) / 500 ]

≈ 0.0222

For n = 1000

= sqrt[(0.55)(0.45) / 1000 ]

≈ 0.0157