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:

Type I Error

The incorrect rejection of a true null hypothesis, also known as a "false positive."

Type II Error

The error that occurs when a statistical test fails to reject a false null hypothesis, also known as a "false negative."

Confidence Interval

A range of values, derived from sample statistics, that is believed to cover the true population parameter with a specified level of confidence.

Democratic Candidate

An individual seeking nomination or election within the Democratic Party, one of the two major political parties in the United States.