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

question 92

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 (x₁in $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?

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Definitions:

Standard Cost

A predetermined cost of manufacturing, which is often used for budgeting and measuring performance.

Purchase Price Variances

The difference between the actual cost of purchased inventory and its standard or expected cost.

Currently Attainable Standard

This refers to a standard or benchmark that can be achieved under current operating conditions with reasonable efficiency.

Unfavorable Cost Variance

A variance that occurs when the actual cost exceeds the standard cost.