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

question 106

Multiple Choice

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 $H _ { 0 } : \beta _ { 2 } = 0 \mathrm { vs } . H _ { \mathrm { a } } : \beta _ { 2 } > 0$ is $.02$ . What is the proper conclusion?

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

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Definitions:

Manufacturing Overhead Account

An account that tracks indirect production costs, such as utilities and rent for manufacturing facilities.

Work in Process

Inventory items that are partially completed but not yet ready for sale; represents goods in various stages of production.

Predetermined Overhead Rate

A rate calculated at the beginning of a period by dividing estimated overhead costs by an estimated activity base, such as labor hours, used to allocate overhead costs to products.

Direct Labor-Hours

A measure of the total hours worked by employees directly involved in the manufacturing process, used as a base for allocating overhead costs.