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. How would you calculate a p value?. Use the alpha of 0.01 Scott: X1 93430, S1= 5602, n1=35

Ligonier: X1= 98043, S1=4731 n2= 40

Solution

Let mu1 be the mean for Scott

Let mu2 be the mean for Ligonier

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.

So the p-value= 2*P(Z<-3.82) = 0.0001 (from standard normal table)

Since the p-value is less than 0.01, we reject the null hypothesis.

So we can conclude that there are differences in price