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

question 79

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

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

• A) \(.0016\)
• B) \(.18\)
• C). 36
• D). 05

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Definitions:

MLU

Mean Length of Utterance, a measure used in linguistics to calculate and analyze the complexity of children's language development by averaging the length of their spoken statements.

Chronological Age

The exact age of an individual as measured in years from the date of birth.

Morpheme

The smallest grammatical unit in a language that carries semantic meaning.

Holophrase

A single word used by an infant that expresses a complex idea or request, indicative of early language development.