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?

Question

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?

Quizplus · Accepted Answer

The Answer of 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 Sociologist Studies the Relationship Between a District's Average Score