Question

In a survey, the planning value for the population proportion is p*=.35. how large a sample should be taken to provide a 95% confidence interval with a margin of error of .05 (to the nearest whole number)?

Answer 1

Given:
p* = 0.35, the populatin proportion.
Sp = 0.05, the margin of error

Let n = the size of the sample.

Because the standard error is 0.05, therefore

`\sqrt{ (p(1-p))/(n) } =0.05`

`\sqrt{ (0.35(1-0.35))/(n) } =0.05`

`(0.2275)/(n) =0.05^(2) =0.0025`
n = 0.2275/0.0025 = 91

Answer: The sample size is 91.