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 resluts of the study are shown below.

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 resluts of the study are shown below. Compute a 95% confidence interval for the mean difference

Scott: X₁ 93430, S₁= 5602, n₁=35

Ligonier: X₁= 98043, S₁=4731 n₂= 40

Scott: X₁ 93430, S₁= 5602, n₁=35

Ligonier: X₁= 98043, S₁=4731 n₂= 40

Solution

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

So a 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.