A Sociologist Studies the Relationship Between a District's Average Score

question 15

Essay

A sociologist studies the relationship between a district's average score on a standardized test for 10th grade students (y), the average school expenditures per student (x₁ in $1,000s), and an index of socioeconomic status of the district (x₂). The results of the regression are = 10.16 + 8.50x₁ + 4.30x₂; n = 25; SSE = 450;
He would like to determine whether the influence of expenditures on test scores differs from the influence of the index on test scores, or β₁ ≠ β₂. The results of the restricted model for this test are = 12.25 + 6.05(x₁ + x₂); n = 25; SSE = 600.
A) Formulate the hypotheses to determine whether Expenditures and Index Rate have the same influence on Scores.
B) Calculate the value of the test statistic.
C) At the 5% significance level, find the critical value(s).
D) What is the conclusion to the test?

• A) Formulate the hypotheses to determine whether Expenditures and Index Rate have the same influence on Scores.
• B) Calculate the value of the test statistic.
• C) At the 5% significance level, find the critical value(s).
• D) What is the conclusion to the test?

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Definitions:

Inputs

Resources used in the production process to create goods and services, including labor, capital, materials, and energy.

Output

The quantity of goods or services produced by a company, industry, or economy within a specified time period.

Constant Returns to Scale

A situation in production where increasing all inputs by a certain proportion results in output increasing by that same proportion.

Verson Stamping Machine

A specific brand or type of machine used in the metal forming process, capable of shaping or cutting metal with high precision through stamping.