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

2401

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 =
`(std dev)/(√(n) ) \\=(1000)/(√(n) )`

Together we get

`40=1.96((1000)/(√(n) ) )\\√(n) =(1000*1.96)/(40) \\=49\\n=2401\\`