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?

---

Definitions:

Employment Programs

Initiatives designed to help individuals find, secure, and retain jobs, often targeting specific groups such as the unemployed or underemployed.

March of Dimes

A nonprofit organization that works to improve the health of mothers and babies by preventing birth defects, premature birth, and infant mortality.

Socio-economic

Pertains to or involves both social and economic factors.

Support

The provision of assistance or encouragement to individuals or groups, often aimed at helping them cope with difficulties.