HOUSING PRICES IN LEXINGTON, MASSACHUSETTS

VALMAX is one of the largest real estate companies in New England. John Porter is the manager of VALMAXs Lexington, Massachusetts office, which is one of their most profitable offices. VALMAX has received complaints from a number of their recent clients in Lexington who believe that they were advised to post asking-prices for their houses that were too low, especially relative to the asking-prices for houses brokered by other realtors.

VALMAX has also received complaints from other clients in Lexington who believe that they were advised to accept selling-prices for houses that they purchased that were too high relative to the selling-prices for houses brokered by other realtors. John Porter has decided to perform an analysis of recent real estate transactions in Lexington in order to estimate the truthfulness of these claims.

Asking-prices and selling-prices of houses sold are public information, and John has obtained this data from the Lexington Town Hall. John has collected the asking prices and selling-prices for the 79 housing sales in Lexington in the last three months, and has divided the sales into the 35 sales brokered by VALMAX and the other 44 sales that were brokered by other realtors. The price data for these two sets of housing sales are contained in the spreadsheet VALMAX.XLS.

Are the clients complaints justified?

1. (25 points) Are the clients complaints justified??
2. (15 points) How much more data should John collect to be 99% confident of his analysis.

House# Asking Price Selling price Difference 1 295, 000 280,000 15,000 2 425,000 411, 000 14, 000 3 299,000 285,000 14,000 4 299,000 299,000 0 5 475,000 471, 000 4, 000 6 350,000 348,000 2,000 7 429,000 418, 000 11,000 8 399,000 401, 000 2,000 9 489,000 476,000 13,000 10 299,000 270,000 29, 000 11 539, 000 531, 000 8,000 12 225,000 214,000 11,000 13 749, 000 735,000 14,000 14 689, 000 664, 000 25,000 15 469, 000 476,000 7,000 16 299,000 270,000 29,000 17 539,000 531, 000 8,000 18 199,000 205,000 6,000 19 349,000 335, 000 14,000 20 689,000 687,000 2,000 21 485, 000 479, 000 6,000 22 299,000 285, 000 14, 000 23 305,000 275,000 30,000 24 479, 000 469, 000 10,000 25 699,000 677,000 22, 000 26 339,000 325,000 14,000 27 195, 000 209,000 14,000 28 539,000 535, 000 4, 000 29 279, 000 268,000 11,000 30 459,000 469,000 10,000 31 679, 000 659, 000 20,000 32 729, 000 725,000 4,000 33 215,000 214,000 1,000 34 539,000 525, 000 14, 000 35 289, 000 270,000 19,000 36 479, 000 469,000 10,000 37 389,000 390,000 1,000 38 419, 000 410,000 9,000 39 339,000 339,000 0 40 469, 000 462,000 7,000 41 299,000 280,000 19,000 42 289, 000 280,000 9,000 43 419, 000 403, 000 16,000 44 289,000 275,000 14,000 House# Asking Price Selling price Difference 1 295, 000 280,000 15,000 2 425,000 411, 000 14, 000 3 299,000 285,000 14,000 4 299,000 299,000 0 5 475,000 471, 000 4, 000 6 350,000 348,000 2,000 7 429,000 418, 000 11,000 8 399,000 401, 000 2,000 9 489,000 476,000 13,000 10 299,000 270,000 29, 000 11 539, 000 531, 000 8,000 12 225,000 214,000 11,000 13 749, 000 735,000 14,000 14 689, 000 664, 000 25,000 15 469, 000 476,000 7,000 16 299,000 270,000 29,000 17 539,000 531, 000 8,000 18 199,000 205,000 6,000 19 349,000 335, 000 14,000 20 689,000 687,000 2,000 21 485, 000 479, 000 6,000 22 299,000 285, 000 14, 000 23 305,000 275,000 30,000 24 479, 000 469, 000 10,000 25 699,000 677,000 22, 000 26 339,000 325,000 14,000 27 195, 000 209,000 14,000 28 539,000 535, 000 4, 000 29 279, 000 268,000 11,000 30 459,000 469,000 10,000 31 679, 000 659, 000 20,000 32 729, 000 725,000 4,000 33 215,000 214,000 1,000 34 539,000 525, 000 14, 000 35 289, 000 270,000 19,000 36 479, 000 469,000 10,000 37 389,000 390,000 1,000 38 419, 000 410,000 9,000 39 339,000 339,000 0 40 469, 000 462,000 7,000 41 299,000 280,000 19,000 42 289, 000 280,000 9,000 43 419, 000 403, 000 16,000 44 289,000 275,000 14,000