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SCENARIO 13-15
the Superintendent of a School District Wanted to Predict

question 185

True/False

SCENARIO 13-15
The superintendent of a school district wanted to predict the percentage of students passing a sixth- grade proficiency test.She obtained the data on percentage of students passing the proficiency test (% Passing), mean teacher salary in thousands of dollars (Salaries), and instructional spending per pupil in thousands of dollars (Spending) of 47 schools in the state.
Following is the multiple regression output with Y = % Passing as the dependent variable,
X1 =
Salaries and
X 2 = Spending:  Regression Statistics  Multiple R 0.4276 R Square 0.1828 Adjusted R Square 0.1457 Standard Error 5.7351 Observations 47 ANOVA df SS  MS  F  Significance F Regression 2323.8284161.91424.92270.0118 Residual 441447.209432.8911 Total 461771.0378 Coefficients  Standard Error t Stat  P-value  Lower 95%  Upper 95%  Intercept 72.991645.91061.58990.1190165.518419.5352 Salary 2.79390.89743.11330.00320.98534.6025 Spending 0.37420.97820.38250.70391.59722.3455\begin{array}{l}\begin{array} { l r } \hline { \text { Regression Statistics } } \\\hline \text { Multiple R } & 0.4276 \\\text { R Square } & 0.1828 \\\text { Adjusted R Square } & 0.1457 \\\text { Standard Error } & 5.7351 \\\text { Observations } & 47 \\\hline\end{array}\\\\\text { ANOVA }\\\begin{array} { l r r r r r } \hline & d f & { \text { SS } } & { \text { MS } } & \text { F } & { \text { Significance } F } \\\hline \text { Regression } & 2 & 323.8284 & 161.9142 & 4.9227 & 0.0118 \\\text { Residual } & 44 & 1447.2094 & 32.8911 & & \\\text { Total } & 46 & 1771.0378 & & & \\\hline\end{array}\\\\\begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & - 72.9916 & 45.9106 & - 1.5899 & 0.1190 & - 165.5184 & 19.5352 \\\text { Salary } & 2.7939 & 0.8974 & 3.1133 & 0.0032 & 0.9853 & 4.6025 \\\text { Spending } & 0.3742 & 0.9782 & 0.3825 & 0.7039 & - 1.5972 & 2.3455 \\\hline\end{array}\end{array}
-Referring to SCENARIO 13-15, you can conclude definitively that instructional spending per pupil individually has no impact on the mean percentage of students passing the proficiency test, considering the effect of mean teacher salary, at a 1% level of significance based solely on but not actually computing the 99% the confidence interval estimate for β\beta 2 .

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