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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View Full Documentnot 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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 Winter '09
 Havenner
 Normal Distribution, Standard Deviation, Statistical hypothesis testing, sq ft, sq ft house, sq foot house

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