A real estate agent compares the selling prices of randomly

A real estate agent compares the selling prices of randomly selected homes in two municipalities in southwestern Pennsylvania to see if there is a difference. The results of the study are shown. Is there enough evidence to reject the claim that the average cost of a home in both locations is the same? Use a=0.01. Scott: Xbar = 93,430, standard deviation = 5602, n= 35. Ligioner: Xbar= 98043, standard deviation= 4731, n=40.

Solution

Let mu1 be the mean for Scott

Let mu2 be the mean for Ligioner

The test hypothesis:

Ho: mu1=mu2 (i.e. null hypothesis)

Ha: mu1 not equal to mu2 (i.e. alternative hypothesis)

The test statistic is

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

=(93430-98043)/sqrt(5602^2/35+4731^2/40)

=-3.82

It is a two-tailed test.

Given a=0.01, the critical values are Z(0.005) = -2.58 or 2.58 (from standard normal table)

The rejection regions are if Z<-2.58 or Z>2.58, we reject the null hypothesis.

Since Z=-3.82 is less than -2.58, we reject the null hypothesis.

So we can conclude that there is enough evidence to reject the claim that the average cost of a home in both locations is the same