A sociologist wants to determine the current population of US households that use e-mail. According to a study conducted five years ago, 76% of households were using e-mail. The sociologist would like to find out how many households must be surveyed to be 95% confident (z*-score = 1.96) that the current estimated population proportion is within a 2% margin of error. Use the formula n = (1 – ) • .How many households must be surveyed to be 95% confident that the current estimated population proportion is within a 2% margin of error?
Accepted Solution
A:
The given data are: E = 2% = 0.02 z = 1.96 p = 72% = 0.72
Start from the margin of error formula:
E = z [tex] \sqrt{ \frac{p(1-p)}{n} } [/tex]
And solve for n = sample size
n = (z/E)² · p · (1-p) = (1.96 / 0.02)² · 0.76 · (1 - 0.76) = 1751.7696
You need to round up to the nearest integer (because you cannot survey half of a person...); the correct answer is: you need to survey 1752 housholds.