Question

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?

Answer 1

1752

Explanation:

edgu 2020

Answer 2

The given data are:
E = 2% = 0.02
z = 1.96
p = 72% = 0.72

Start from the margin of error formula:

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

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.