SCENARIO 12-13
in This Era of Tough Economic Conditions, Voters

question 52

Short Answer

SCENARIO 12-13
In this era of tough economic conditions, voters increasingly ask the question: "Is the educational achievement level of students dependent on the amount of money the state in which they reside spends on education?" The partial computer output below is the result of using spending per student ($) as the independent variable and composite score which is the sum of the math, science and reading scores as the dependent variable on 35 states that participated in a study.The table includes only partial results. $$\begin{array}{l}\begin{array} { l c } \hline { \text { Regression Statistics } } \\\hline \text { Multiple R } & 0.3122 \\\text { R Square } & 0.0975 \\\text { Adjusted R } & 0.0701 \\\text { Square } & \\\text { Standard } & 26.9122 \\\text { Error } & \\\text { Observations } & 35 \\\hline\end{array}\\\end{array}$$
ANOVA
$\begin{array}{lccc}& d f & S S & M S & F \\\text { Regression } & 1 & 2581.5759 & \\\text { Residual } & & & 724.2674 \\\text { Total } & 34 & 26482.4000 &\end{array}$
$$\begin{array}{l}\begin{array} { l c c c c } \hline & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & P \text {-value } \\\hline \text { Intercept } & 595.540251 & 22.115176 & & \\\text { Spending per } & & & & \\\text { Student(\$) } & 0.007996 & 0.004235 & \\\hline\end{array}\end{array}$$
-Referring to Scenario 12-13, the p-value of the measured F-test statistic to test whether spending per student affects composite score is .

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Definitions:

Squared Deviations

The squared differences between individual values and the mean of a dataset, used in statistical analysis to measure variance.

Scatter Diagram

A visual depiction employing points to illustrate the connection between two numerical variables.

Cov(X,Y)

The covariance between two variables X and Y, measuring how changes in one variable are associated with changes in the other.

Sample Slope Coefficient

A parameter in a linear regression equation that represents the change in the dependent variable for a one-unit change in the independent variable.