A Collector of Grandfather Clocks Believes That the Price Received $$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }$$

question 61

Short Answer

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 $$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }$$
This model was fit to data collected for a sample of 32 clocks sold at auction.
Suppose the $p$ -value for the test of $H _ { 0 } : \beta _ { 2 } = 0$ vs. $H _ { \mathrm { a } } : \beta _ { 2 } > 0$ is .02. What is the proper conclusion?
A) There is evidence (at $\alpha = .05$ ) of upward curvature in the relationship between auction price $( y )$ and number of bidders $( x )$ .
B) There is no evidence (at $\alpha = .05$ ) of upward curvature in the relationship between auction price (y) and number of bidders $( x )$ .
C) Reject $H _ { 0 }$ at $\alpha = .05$ ; the model is not useful for predicting auction price $( y )$ .
D) There is evidence (at $\alpha = .05$ ) of downward curvature in the relationship between auction price $( y )$ and number of bidders $( x )$ .

• A) There is evidence (at \(\alpha = .05\) ) of upward curvature in the relationship between auction price \(( y )\) and number of bidders \(( x )\).
• B) There is no evidence (at \(\alpha = .05\) ) of upward curvature in the relationship between auction price (y) and number of bidders \(( x )\).
• C) Reject \(H _ { 0 }\) at \(\alpha = .05\); the model is not useful for predicting auction price \(( y )\).
• D) There is evidence (at \(\alpha = .05\) ) of downward curvature in the relationship between auction price \(( y )\) and number of bidders \(( x )\).

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Definitions:

Balance

In accounting, balance refers to the difference between the sum of debits and credits in an account, often shown on financial statements like the balance sheet.

Aggressive Revenue Recognition

A practice where revenue is recognized before it meets the criteria for recognition, often inflating financial performance.

Liberal Return Policy

A company policy that allows customers to return purchased items with minimal restrictions, aiming to enhance customer satisfaction and trust.

Recognizes Revenue

The process of recording revenue in the financial statements when it is earned and realizable.