Home values tend to increase over time under normal conditions, but the recession of 2008 and 2009 has reportedly caused the sales price of existing homes to change nationwide.† You would like to see if the data support this conclusion. Data on 30 existing home sales in 2006 and 40 existing home sales in 2009 gives the following information. 2006 2009 n1 = 30 n2 = 40 x1 = $224,003 x2 = $174,440 s1 = $56,485 s2 = $46,356 (a) Provide a point estimate of the difference (in dollars) between the population mean prices for the two years. (Use year 2006 ? year 2009. Round your answer to the nearest dollar.) $ (b) Suppose that the degrees of freedom has been calculated and found to be df = 55 . Develop a 99% confidence interval estimate of the difference (in dollars) between the resale prices of houses in 2006 and 2009. (Use year 2006 ? year 2009. Round your answers to the nearest dollar.) $ to $ (c) Would you feel justified in concluding that resale prices of existing homes have changed from 2006 to 2009? Why or why not? To answer this question, we will conduct a hypothesis test. State the null and alternative hypotheses. (Let ????1 = mean home price in 2006 and let ????2 = mean home price in 2009.) H0: ????1 ? ????2 <= 0 Ha: ????1 ? ????2 > 0 H0: ????1 ? ????2 != 0 Ha: ????1 ? ????2 = 0 H0: ????1 ? ????2 >= 0 Ha: ????1 ? ????2 < 0 H0: ????1 ? ????2 = 0 Ha: ????1 ? ????2 > 0 H0: ????1 ? ????2 = 0 Ha: ????1 ? ????2 != 0 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. (Use ???? = 0.01) Do not reject H0. We can conclude that existing home prices have changed between 2006 and 2009. Reject H0. We can not conclude that existing home prices have changed between 2006 and 2009. Do not reject H0. We can not conclude that existing home prices have changed between 2006 and 2009. Reject H0. We can conclude that existing home prices have changed between 2006 and 2009.