ARE 106 HW 5

# ARE 106 HW 5 - Jeff Phang ARE 106 HW 5#1 i The value 2.179...

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Jeff Phang ARE 106 HW # 5 #1. i). The value 2.179 in the “generate” statements is the critical # of standard deviations from the true value of the Y values to create a confidence interval. ii). Estimated mean for a 2000 sq ft house: Price = 52.3509 + 0.138750 (sq ft) Price = 52.3509 + 0.138750 (2000 sq ft) = 329.8509 Using equation 3.29: Since we’re predicting the mean price of a house in the area for the government we will use the standard error of s 2 y hato = 111.555. s y hato = √ 111.555= 10.562 P(Y hat – t (0.025, 12) (sy hato ) < E(Yo) < Y hat + t (0.025, 12) (sy hato )) = .95 P(Price hat – 2.179(sy hato ) < E(Yo)< Price hat + 2.179(sy hato )) = .95 P(329.851 – 2.179(10.562)< E(Yo) < 329.851 – 2.179(10.562) = .95 P(306.8364 < Yo < 352.8656) = .95 We’re 95% confident that the price of a 2000 sq foot house is between \$306,836 and \$352,865. iii). Ho: Price near airport = Price bar away from airport Ha: Price near airport < Price bar away from airport Price hat o = 329.8509 Price of house = 220.0000 Test statistic = 220.0000 – 329.8509 / 40.427= -2.717126 Tc (12, 0.05) = 1.78 |T*| < Tc therefore we reject the null hypothesis. The sale price was significantly affected by the construction of the airport runway relative to the houses that are not by the runway. Tc(12, 0.025) = 2.179 P(price hat – 2.179(σu hat )< Price bar < price hat + 2.179(σu hat )) = .95 P(329.8509 – 2.179(40.427) < Price bar < 329.8509 + 2.179(40.427)) = .95 P(241.76 < Price near runway < 417.942) = .95 The house price was influenced by the airport construction. I can say with 95% certainty that the price of a 2000 sq ft house would be within \$241,760 and \$417,941 for a house

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not affected by external factors like the airport construction. The price of \$220,000 is out of this range so it would appear that the construction had an adverse affect on the price. This price would happen by chance alone only 5% of the time if the construction really
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ARE 106 HW 5 - Jeff Phang ARE 106 HW 5#1 i The value 2.179...

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