A Collector of Grandfather Clocks Believes That the Price Received $y$

question 32

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; a portion of the printout follows:

$\begin{array}{lrrrr}&\text { PARAMETER}&\text { STANDARD }&\text { TFOR } 0 \text { : }\\\text { VARIABLES}& \text { ESTIMATE } &\text { ERROR }& \text { PARAMETER }=0 & \text { PROB }>|\mathrm{T}|\\\\\text { INTERCEPT } & 286.42 & 9.66 & 29.64 & .0001 \\X & -.31 & .06 & -5.14 & .0016 \\\mathrm{X} \cdot \mathrm{X} & .000067 & .00007 & .95 & .3600 \\\hline\end{array}$


Find the $p$ -value for testing $H _ { 0 } : \beta _ { 2 } = 0$ against $H _ { \mathrm { a } } : \beta _ { 2 } > 0$ .

• A) .18
• B) .05
• C) .0016
• D) .36

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Definitions:

Economic Return

The profit or loss generated on an investment over a specific period, considering both cash flow and changes in market value.

Time Value of Money

A financial principle that money available today is worth more than the same amount in the future due to its potential earning capacity.

Operating Costs

Expenses associated with the operation and maintenance of a business or asset, excluding taxes and interest costs.

Rate of Return

The gain or loss on an investment over a specified period, expressed as a percentage of the investment's initial cost.