Instruction 12 $\text { Regressing average grade on university entrance exam score }$

question 121

Multiple Choice

Instruction 12.32
It is believed that average grade (based on a four-point scale) should have a positive linear relationship with university entrance exam scores. Given below is the Microsoft Excel output from regressing average grade on university entrance exam scores using a data set of eight randomly chosen students from a large university.
$\text { Regressing average grade on university entrance exam score }$

$\text { Regression statistics }$
$\begin{array}{|l|l|}\hline\text { MultipleR } & 0.7598 \\\hline \text { R Square } & 0.5774 \\\hline \begin{array}{l}\text { Adjusted R } \\\text { Square }\end{array} & 0.5069 \\\hline \text { Standard Error } & 0.2691 \\\hline \text { Observations } & 8\\\hline\end{array}$

$\text { ANOVA }$
$\begin{array}{|l|l|l|l|l|l|}\hline & d f & 55 & M S & F & \begin{array}{l}\text { Significance } \\F\end{array} \\\hline \text { Regression } & 1 & 0.5940 & 0.5940 & 8.1986 & 0.0286 \\\hline \text { Residual } & 6 & 0.4347 & 0.0724 & & \\\hline \text { Total } & 7 & 1.0287 & & & \\\hline\end{array}$

$\begin{array}{|l|l|l|l|l|l|l|}\hline & \text { Coefficients } & \begin{array}{l}\text { Standard } \\\text { Error }\end{array} & \text { tStat } & \text { p-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 0.5681 & 0.9284 & 0.6119 & 0.5630 & -1.7036 & 2.8398 \\\hline \begin{array}{l}\text { University } \\\text { entrance exam } \\\text { score }\end{array} & 0.1021 & 0.0356 & 2.8633 & 0.0286 & 0.0148 & 0.1895 \\\hline\end{array}$
-Referring to Instruction 12.32,what are the decision and conclusion on testing whether there is any linear relationship at 1% level of significance between average grade and university entrance exam scores?

• A) Do not reject the null hypothesis; hence there is not sufficient evidence to show that university entrance exam scores and average grade are linearly related.
• B) Reject the null hypothesis; hence there is not sufficient evidence to show that university entrance exam scores and average grade are linearly related.
• C) Reject the null hypothesis; hence there is sufficient evidence to show that university entrance exam scores and average grade are linearly related.
• D) Do not reject the null hypothesis; hence there is sufficient evidence to show that university entrance exam scores and average grade are linearly related.

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Definitions:

Inductive Argument

A form of reasoning in which the premises provide some evidence, but not full assurance, of the truth of the conclusion.

Analogy

Analyzing the similarities or differences between two items, usually to explain or make something clearer.

Identical

Exactly the same, without any difference.

Generalization

The process of extracting common characteristics from specific examples, leading to a broad conclusion or principle.