As Part of a Study at a Large University, Data $n = 224$

question 100

Multiple Choice

As part of a study at a large university, data were collected on $n = 224$ freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling $y$ , a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university) :
$x _ { 1 } =$ average high school grade in mathematics (HSM)
$x _ { 2 } =$ average high school grade in science (HSS)
$x _ { 3 } =$ average high school grade in English (HSE)
$x _ { 4 } =$ SAT mathematics score (SATM)
$x _ { 5 } =$ SAT verbal score (SATV)

A first-order model was fit to data with the following results:

$\begin{array}{lrrrrr}\hline \text { SOURCE } & \text { DF } & \text { SS } & \text { MS } & \text { F VALUE } & \text { PROB > F } \\\text { MODEL } & 5 & 28.64 & 5.73 & 11.69 & .0001 \\\text { ERROR } & 218 & 106.82 & 0.49 & & \\\text { TOTAL } & 223 & 135.46 & & &\end{array}$


$\begin{array}{lccc}\text { ROOT MSE } & 0.700 & \text { R-SQUARE } & 0.211 \\\text { DEP MEAN } & 4.635 & \text { ADJR-SQ } & 0.193\end{array}$
$\begin{array}{l}\begin{array} { l r r r r } & \text {PARAMETER }& \text {STANDARD}& \text {T FOR 0:}\\ \text {VARIABLES}&\text { ESTIMATE } & \text { ERROR } & \text { PARAMETER } = 0 & \text { PROB } > | T | \\ \\\text { INTERCEPT } & 2.327 & 0.039 & 5.817 & 0.0001 \\\text { X1 (HSM) } & 0.146 & 0.037 & 3.718 & 0.0003 \\\text { X2 (HSS) } & 0.036 & 0.038 & 0.950 & 0.3432 \\\text { X3 (HSE) } & 0.055 & 0.040 & 1.397 & 0.1637 \\\text { X4 (SATM) } & 0.00094 & 0.00068 & 1.376 & 0.1702 \\\text { X5 (SATV) } & - 0.00041 & 0.00059 & - 0.689 & 0.4915 \\\hline\end{array}\end{array}$

Interpret the value under the column heading $P R O B > F$ .

• A) Accept \(H _ { 0 }\) (at \(\alpha = .01\) ); at least one of the \(\beta\)-coefficients in the first-order model is equal to 0 .
• B) Over \(99 \%\) of the variation in GPAs can be explained by the model.
• C) There is insufficient evidence (at \(\alpha = .01\) ) to conclude that the first-order model is statistically useful for predicting GPA.
• D) There is sufficient evidence (at \(\alpha = .01\) ) to conclude that the first-order model is statistically useful for predicting GPA.

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Definitions:

Priming Task

A technique in psychology used to train or influence participants' responses towards a subsequent task, by exposing them to specific stimuli beforehand.

Metaphor Priming Procedure

This is a cognitive method used in psychological research to influence how individuals process information, by subtly introducing metaphors that can shape thinking and responses.

Explicit Attitudes

Attitudes that are consciously recognized and expressed by individuals, often through verbalization.

Implicit Attitudes

Unconscious beliefs or feelings towards objects, people, or situations, which can influence behavior and understanding without conscious awareness.