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

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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 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 (x<sub>1</sub> in $1,000s), and an index of socioeconomic status of the district (x<sub>2</sub>). The results of the regression are = 10.16 + 8.50x<sub>1</sub> + 4.30x<sub>2</sub>; 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 β<sub>1</sub> ≠ β<sub>2</sub>. The results of the restricted model for this test are = 12.25 + 6.05(x<sub>1</sub> + x<sub>2</sub>); 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? = 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 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 (x<sub>1</sub> in $1,000s), and an index of socioeconomic status of the district (x<sub>2</sub>). The results of the regression are = 10.16 + 8.50x<sub>1</sub> + 4.30x<sub>2</sub>; 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 β<sub>1</sub> ≠ β<sub>2</sub>. The results of the restricted model for this test are = 12.25 + 6.05(x<sub>1</sub> + x<sub>2</sub>); 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? = 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?

Correct Answer:

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a. H0: β1 = β2; HA:β1 ≠ β2
b. F(1,22) = 7.33
c. Usin...

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