Case Problem: Government (State) Spending And Student Achievement
Is the educational achievement level of students related to how much the state in which they reside spends on education? In many communities this important question is being asked by taxpayers who are being asked by their school districts to increase the amount of tax revenue spent on education. In this case, you will be asked to analyze data on state spending and achievement scores in order to determine whether there is any relationship between government spending and student achievement in the public schools.
The federal government's National Assessment of Educational Progress (NAEP) program is frequently used to measure the educational achievement of students. The Excel spreadsheet: Student Spending Achievement Data and Worksheet 1 (35 states tab) shows the total current spending per pupil per year, and the composite NAEP test score for 35 states that participated in the NAEP program. The composite score is the sum of the math, science, and reading scores on the 1996 (1994 for reading) NAEP test. Pupils tested are in grade 8, except for reading, which is given to fourth-graders only. The maximum possible score is 1300.
Please view the attached file presenting the data in order to answer the following questions:
Questions:
a. Develop numerical and graphical summaries of the data.
b. Use regression analysis to investigate the relationship between the amount spent per pupil and the composite score on the NAEP test. Discuss your findings.
c. Do you think that the estimated regression equation developed for these data could be used to estimate the composite scores for the states that did not participate in the NAEP program?
d. Suppose that you only considered states that spend at least $4000 per pupil but not more than $6000 per pupil. For these states, does the relationship between the two variables appear to be any different than for the complete data set? Discuss the results of your findings and whether you think deleting states with spending less than $4000 per year and more than $6000 per pupil is appropriate.
e. Develop estimates of the composite scores for the states that did not participate in the NAEP program.
f. Based upon your analyses, do you think that the educational achievement level of students is related to how much the state spends on education?
https://brainmass.com/statistics/regression-analysis/case-problem-government-state-spending-and-student-achievement-19896
Solution Preview
a. Develop numerical and graphical summaries of the data.
Please refer to the EXCEL file.
b. Use regression analysis to investigate the relationship between the amount spent per pupil and the composite score on the NAEP test. Discuss your findings.
From the EXCEL file, the OLS regression of composite score on government spending is:
Score = 587.32 + 0.00865* spending.
This means that for each $1 more spending on per student, their average score can be increased by 0.00865.
The t stat of both coefficients are greater than 2.0, so the coefficient estimates are significant.
c. Do you think that the estimated regression equation developed for these data could be used to estimate the composite scores for the states that did not participate in the NAEP program?
If the government spending is ...
Solution Summary
This solution provides a detailed, step by step response which is provided using both a Word document and an Excel file. These attachments are accompanying this solution.