# Spending and Student Achievement Case

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Spending and Student Achievement Case (Correlation between variables, examine magnitude and meaning of residuals, evaluation and application of linear regression in a business example).

Read Case Problem ?Government (State) Spending and Student Achievement? below. Be sure to read the case thoroughly, analyze the raw data, and help explain how to answer all questions as required per case instructions. (Reference: Anderson, Sweeney, Williams, 2002, p. 264). Cut and paste your results from EXCEL into your paper.

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.

The Excel spreadsheet: Student Spending Achievement Data and Worksheet 2 (13 states tab) shows the spending per pupil for 13 states that did not participate in relevant NAEP surveys. These data were reported in an article on spending and achievement level appearing in Forbes (November 3, 1997).

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?

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##### Solution Summary

Spending and Student Achievement Case (Correlation between variables, examine magnitude and meaning of residuals, evaluation and application of linear regression in a business example).

Read Case Problem ?Government (State) Spending and Student Achievement? below. Be sure to read the case thoroughly, analyze the raw data, and help explain how to answer all questions as required per case instructions. (Reference: Anderson, Sweeney, Williams, 2002, p. 264). Cut and paste your results from EXCEL into your paper.

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.

The Excel spreadsheet: Student Spending Achievement Data and Worksheet 2 (13 states tab) shows the spending per pupil for 13 states that did not participate in relevant NAEP surveys. These data were reported in an article on spending and achievement level appearing in Forbes (November 3, 1997).

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?

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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