A real estate agent compares the selling prices of homes in

A real estate agent compares the selling prices of homes in two municipalities in southwestern Pennsylvania to see if there are differences in price. The results of the study are shown below. Compute a 95% confidence interval for the mean difference

Scott: X₁=93430; S₁=5602; n1=35

Ligonier: X₂=98043; S₂=4731; n2=40

Solution

Given a=0.05, Z(0.025) = 1.96 (from standard normal table)

So 95% confidence interval for the mean difference is

(xbar1-xbar2) +/- Z*sqrt(s1^2/n1+s2^2/n2)

--> (93430-98043) +/- 1.96*sqrt(5602^2/35+4731^2/40)

--> (-6978.192, -2247.808)

Since the interval does not include 0, we can conclude that there are differences in price.