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

question 258

Short Answer

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: $$\begin{array}{l}\begin{array} { l r } \hline { \text { Regression Statistics } } \\\hline \text { Multiple R } & 0.4276 \\\text { R Square } & 0.1828 \\\text { Adjusted R Square } & 0.1457 \\\text { Standard Error } & 5.7351 \\\text { Observations } & 47 \\\hline\end{array}\\\text { ANOVA }\\\begin{array} { l r r r r r } \hline & d f & { \text { SS } } &{ \text { MS } } & \text { F } & { \text { Significance } F } \\\hline \text { Regression } & 2 & 323.8284 & 161.9142 & 4.9227 & 0.0118 \\\text { Residual } & 44 & 1447.2094 & 32.8911 & & \\\text { Total } & 46 & 1771.0378 & & & \\\hline\end{array}\\\\\begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & - 72.9916 & 45.9106 & - 1.5899 & 0.1190 & - 165.5184 & 19.5352 \\\text { Salary } & 2.7939 & 0.8974 & 3.1133 & 0.0032 & 0.9853 & 4.6025 \\\text { Spending } & 0.3742 & 0.9782 & 0.3825 & 0.7039 & - 1.5972 & 2.3455 \\\hline\end{array}\end{array}$$
-Referring to SCENARIO 13-15, which of the following is the correct null hypothesis to test whether instructional spending per pupil has any effect on percentage of students passing the proficiency test, considering the effect of mean teacher salary? a) $H _ { 0 } : \beta _ { 0 } = 0$
b) $H _ { 0 } : \beta _ { 1 } = 0$
c) $H _ { 0 } : \beta _ { 2 } = 0$
d) $H _ { 0 } : \beta _ { 3 } = 0$

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