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Chapter 13: Problem 15

Is there a correlation between state and federal spending on education? The following output shows the regression analysis on state and federal spending on education from a sample of states. Assume the conditions for the linear regression model are satisfied. Show all 4 steps of the hypothesis test.

Short Answer

Expert verified
To answer if there is a correlation between state and federal spending on education, conduct a hypothesis test with 4 steps: stating the hypotheses, formulating an analysis plan, analyzing sample data, and interpreting the results. To reject the null hypothesis, the P-value needs to be smaller than the significance level.

Step by step solution

01

State the Hypotheses

The null hypothesis will be that there is no correlation between state and federal spending on education. In statistical terms, this implies that the population correlation coefficient, \(\rho\) (rho), is zero. The alternative hypothesis is the opposite of the null hypothesis; it is what you might believe is true or hope to prove true, which here would be that there is a correlation between state and federal spending on education. In statistical terms, this implies that the population correlation coefficient, \(\rho\) (rho), is not zero.
02

Formulate an Analysis Plan

The analysis plan includes the significance level and the test statistic. A commonly used significance level is 0.05. For this hypothesis test, the test statistic is a t-score (t). The degrees of freedom (df) for this test is \(n - 2\), where \(n\) is the number of pairs of data.
03

Analyze Sample Data

Using sample data, calculate the value of the test statistic. In this step, regression analysis results will be needed to compute the test statistic value.
04

Interpret the Results

Since the test statistic is a t-score, use the T-Distribution to find the P-Value associated with the observed value of the test statistic. If the P-Value is smaller than the significance level, you reject the null hypothesis.

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