Question

Five years ago, the average apartment rent in southwest Virginia was $895 per month. A recent study of 180 randomly selected apartments found that the average rent was $915, with a standard deviation of $227.50. Do the data enable us to conclude that rents have increased? What is the 97.5% confidence interval for the population mean?

Answer 1

Solution:

Given :

n= 180 sample size

. Sample mean

s = 227.50 sample standard deviations

level of significance

The 97.5% confidence interval for population mean is

. Here n >30 we used  

At

from Z table

( 877.01665, 952.98334)

( 877.01, 952.98)

The 97.5% confidence interval for population mean is

( 877.01, 952.98)

The data do not unable to conclude that rent has increased, because the reference value falls or lies in the confidence interval.