City housing department wants to estimate the average rent f

City housing department wants to estimate the average rent for rent-controlled apartments. They need to determine the number of renters to include in the survey in order to estimate the average rent to within $80 using a 98% confidence interval. From past results, the rent for controlled apartments ranged from $400 to $1600 per month. How many renters are needed in the survey?

Must use the following formula to solve:

n = [(z_a/2 * s) / (E)]² where standard deviation equals 300

Solution

We use (1600-400)/4 =300 as estimated for standard deviation.

Given a=1-0.92=0.08, Z(0.08/2)=1.75 (from standard normal table)

So n=(Z*s/E)^2

=(1.75*300/80)^2

=43.06641

Take n=44