SCENARIO 14-15
the Superintendent of a School District Wanted to Predict

question 248

Short Answer

SCENARIO 14-15
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, $X _ { 1 } =$
Salaries and $X _ { 2 } =$ Spending:

$\begin{array}{lr}\hline {\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.4276 \\\text { R Square } & 0.1828 \\\text { Adjusted R Square } & 0.1457 \\\text { Standard Error } & 5.7351 \\\text { Observations } & 47 \\\hline\end{array}$

ANOVA


$\begin{array}{lrrrrrr}\hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \rho \text {-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -72.9916 & 45.9106 & -1.5899 & 0.1190 & -165.5184 & 19.5352 \\\text { Salary } & 2.7939 & 0.8974 & 3.1133 & 0.0032 & 0.9853 & 4.6025 \\\text { Spending } & 0.3742 & 0.9782 & 0.3825 & 0.7039 & -1.5972 & 2.3455 \\\hline\end{array}$

-Referring to Scenario 14-15, which of the following is the correct null hypothesis to determine whether there is a significant relationship between percentage of students passing the proficiency
Test and the entire set of explanatory variables? a) $H _ { 0 } : \beta _ { 0 } = \beta _ { 1 } = \beta _ { 2 } = 0$
b) $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = 0$
c) $H _ { 0 } : \beta _ { 0 } = \beta _ { 1 } = \beta _ { 2 } \neq 0$
d) $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } \neq 0$

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Definitions:

Public Support

The backing or endorsement by the general population for a person, policy, or initiative.

Non-Controlling Interest

The portion of equity in a subsidiary not attributable directly or indirectly to the parent company, reflecting the minority shareholders' share in the subsidiary's net assets.

Identifiable Net Assets Method

A technique used in business combinations where only the assets and liabilities that can be identified and valued are included in the calculations of the purchase price allocation.

Amortization

The gradual reduction of a debt over a period of time through regular payments covering interest and principal.