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

question 1

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

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

• A) .36
• B) .0016
• C) .18
• D) .05

Analyze the principle of parsimony and its application in preferring theories.

Comprehend the steps involved in the scientific method and the role of hypotheses.

Acknowledge the significance of testable predictions in evaluating scientific theories.

Grasp the concept of falsifiability as a criterion for assessing the scientific viability of theories.

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Definitions:

Consequent

In logic, the consequent is the second part of a conditional statement, typically following "then." For example, in "If P, then Q," Q is the consequent.

Categorical Proposition

A statement that asserts or denies something about every member of a category, involving a subject and a predicate and classified based on quality (affirmative or negative) and quantity (universal or particular).

Hypothetical Proposition

An assumption made for the sake of argument or investigation, often forming the basis of a conditional statement.

Antecedent

In grammar, the word, phrase, or clause that a pronoun or other part of a sentence refers to.