Question

Suppose that you want to estimate average income in a population. If the standard deviation of income in the population is $1,000, approximately how many people do you need to sample in order to have a 95% confidence interval around your estimate of +/- $40?*

Answer 1

Answer:

2401

Step-by-step explanation:

Given that we want to estimate average income in a population.

The standard deviation of income in the population is $1,000

We want confidence interval around our estimate to be +/- $40

i.e Margin of error = 40

We know that margin of error = Std error * Z critical for 95%

i.e. $40 = 1.96 * std error$

Std error = $\frac{std dev}{\sqrt{n} } \\=\frac{1000}{\sqrt{n} }$

Together we get

$40=1.96(\frac{1000}{\sqrt{n} } )\\\sqrt{n} =\frac{1000*1.96}{40} \\=49\\n=2401$