A real estate agency wants to compare the appraised value of single-family homes in two Central Austin neighborhoods. A sample of 39 listings in Rosedale (north central Austin) and 45 listings in Travis Heights (south central Austin) yields the following results (in 1000s of dollars). The sample mean for Rosedale is $340.57 with a standard deviation of $47.80. The sample mean for Travis Heights is $310.19 with a standard deviation of $36.75.
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 neighborhoods? 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 neighborhoods? Remember the values are in thousands, therefore, be sure to express the values in actual dollars once your calculations are complete.
c. What does the confidence interval found in part b tell you about the likelihood that homes in Travis Heights are more expensive than homes in Rosedale? Explain referencing the values you got in part b. No calculations are necessary.