Question 1
A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant) rate. Thus, the model proposed to best explain auction price (
y, in dollars) by number of bidders (
x) is the quadratic model
E(y) = β0 + β1x + β2x2
This model was fit to data collected for a sample of 32 clocks sold at auction; a portion of the printout follows:
Give the
p-value for testing
H0:
β2 = 0 against
Ha:
β2 ≠ 0.
◦ .05
◦ .0016
◦ .18
◦ .36
Question 2
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status the owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model
E(
y) =
β0 +
β1x +
β2x2where
y = Demand (in thousands) and
x = Retail price per carat (dollars).
This model was fit to data collected for a sample of 12 rare gems.
If the experts are correct in their assumptions about the relationship between price and demand, which of the following should be true?
◦
β2 < 0
◦
β1 > 0
◦
β2 > 0
◦
β1 < 0
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