Instruction 12-8
It Is Believed That Average Grade (Based on a Four

question 20

Multiple Choice

Instruction 12-8
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.
Regressing average grade on university entrance exam score
$\begin{array}{lr}\hline {\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.7598 \\\text { R Square } & 0.5774 \\\hline \text { Adjusted R Square } & 0.5069 \\\hline \text { Standard Error } & 0.2691 \\\hline \text { Observations } & 8 \\\hline\end{array}$
ANOVA
$\begin{array}{llllll} & d f & {\text { SS }} & M S & F & \text { Significance F } \\\hline \text { Regression } & 1 & 0.5940 & 0.5940 & 8.1986 & 0.0286 \\\text { Residual } & 6 & 0.4347 & 0.0724 & & \\\text { Total } & 7 & 1.0287 & & &\end{array}$
$\begin{array}{|l|r|r|r|r|r|r|}\hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 0.5681 & 0.9284 & 0.6119 & 0.5630 & -1.7036 & 2.8398 \\\hline \text { University entrance } & & & & & & \\\text { exam score } & 0.1021 & 0.0356 & 2.8633 & 0.0286 & 0.0148 & 0.1895 \\\hline\end{array}$
-Referring to Instruction 12-8,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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