The collapse of the housing bubble in 2008 saw housing prices in the largest cities losing a third of their value, the stock market nearly collapsed, and unemployment doubled. Yet, the story of the recession isn't necessarily one of loss so much as it is of increasing income inequality. While families hovering around the average net worth lost 36% in the decade spanning from 2003 to 2013, people in the top 95th percentile actually gained 14% in the same tumultuous period. In one large community, a random sample of 55 homes found an average loss in home value of $29, 675 from 2003 to 2013 with a standard deviation of approximately $4,000. (8 pts)

a) Use the TInterval command in your calculator to find a 98% confidence interval for the mean loss in home value in this community. To receive credit, write the command and the values you entered. b) Interpret the interval you found in part (a). c) Use the interval you found in part (a) to find the margin of error associated with this confidence interval. d) A government official claims that the mean loss is home value is greater than $28,500, does your interval support this claim? Explain.