A real estate agency wants to compare the appraised value of single-family homes in two Travis County communities. A sample of 40 listings in Shady Hollow (far south) and 62 listings in Balcones Woods (far north) yields the following results (in 1000s of dollars). The sample mean for Shady Hollow is $191.33 with a standard deviation of $32.60. The sample mean for Balcones Woods is $172.34 with a standard deviation of $16.92.
a. At the .05 level of significance, is there evidence of a difference in average appraised values for the single-family homes in the 2 communities? Set up Hypotheses, find p-value and draw verbal conclusion.
b. What is the 95% confidence interval for the difference between population means in the 2 communities?
c. What does this confidence interval tell you about the likelihood that homes in Balcones Woods are more expensive than homes in Shady Hollow? Explain referencing the values you got in part b. No calculations are necessary