SCENARIO 15-1 A certain type of rare gem serves as a status symbol for many of its owners.In theory, for low prices, the demand increases, and it 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 owners believe they gain in obtaining the gem.Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model: where Y = demand (in thousands)and X = retail price per carat. This model was fit to data collected for a sample of 12 rare gems of this type.A portion of the computer analysis obtained from Microsoft Excel is shown below: SUMMARY OUTPUT
-Referring to Scenario 15-1, what is the p-value associated with the test statistic for testing whether there is an upward curvature in the response curve relating the demand (Y)and the price (X)?
A)0.0001
B)0.0006
C)0.3647
D)None of the above.

Question

SCENARIO 15-1 A certain type of rare gem serves as a status symbol for many of its owners.In theory, for low prices, the demand increases, and it 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 owners believe they gain in obtaining the gem.Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:  where Y = demand (in thousands)and X = retail price per carat. This model was fit to data collected for a sample of 12 rare gems of this type.A portion of the computer analysis obtained from Microsoft Excel is shown below: SUMMARY OUTPUT   
-Referring to Scenario 15-1, what is the p-value associated with the test statistic for testing whether there is an upward curvature in the response curve relating the demand (Y)and the price (X)?
A)0.0001 
B)0.0006 
C)0.3647 
D)None of the above.

Quizplus · Accepted Answer

The p-value of 0.3647 suggests that there is not enough evidence to conclude that there is an upward curvature in the response curve, as it is not sufficiently small to reject the null hypothesis of no curvature.

SCENARIO 15-1 a Certain Type of Rare Gem Serves as a Status