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

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