Scenario

For the Final Exam, assume that you are working on a team that has been commissioned by a large school district to collect and analyze data related to a recent curriculum experiment designed to improve student scores on statewide-standardized tests. The schools in this district are predominantly large, urban schools. They are interested in knowing how successful the experiment was and if the new curriculum should be incorporated district-wide. Three years ago, the school district rolled out the experimental curriculum to 100 of the 400 elementary schools in the district. Those 100 schools were selected via a simple random sample. The working budget is not large enough to collect data on the population of 400 schools, and you can only afford to collect a sample of 80 schools. Unless the question states otherwise, conduct all analyses at the 95% confidence level (α=.05).

Section One

You believe the best sampling strategy is stratified sampling. You would like to list the characteristics of schools in this district. You randomly select 80 schools who roughly match the demographic characteristics of the entire population of schools in this district. Forty (40) of these would come from schools that had the experimental curriculum and 40 would come from schools that kept the old curriculum.

However, people from the school board have made the following statements regarding sampling:

1. One well-meaning school board member argued, "… because we are interested in how successful the curriculum is, we should sample the 80 schools with the best results from the experimental curriculum."
2. The school board member who represents one of the poorest neighborhoods said, "… everybody knows that schools in poor neighborhoods are the most in need of reform. Therefore, our sample should be the 80 schools with the lowest household income among students."
3. The school board member who authored the new curriculum told you, "… look, to be honest, the old curriculum was horrible compared to the new one, but many teachers and parents are simply reluctant to change. The Secretary of Education testified in the US Congress that 'this curriculum is quite honestly the best curriculum in the country. It would be foolish not to roll it out to all schools immediately.’ The best thing for our kids is to have the best performing schools with the new curriculum and the worst performing schools with the old curriculum in the sample...the bigger we can make the impact look, the greater the support will be to adopt the new curriculum district wide."

Questions to answer. Describe what is wrong methodologically with each of the three suggestions you received from the various school board members. Writing complete sentences, you need to focus on the following issues:

1. Sampling error (5-points),
2. The sorts of biases that would be introduced from such sampling methods (5-points),
3. How you might expect to see those biases manifested in the data/data analysis (5-points), and
4. How these issues would affect your ability to comment on the district's original question as to whether or not it would be a good idea to roll out the new curriculum to all schools in the district (5-points).

Section Two

Having convinced the board members that a stratified sample is the most appropriate, you collect data from the 80 schools. The spreadsheet provided contains the collected data in the tab labeled "Data." The difference between average school test scores three years ago and average school test scores today is recorded as "chgtestscores." Positive values of chgtestscores indicate an increase in test scores at the school as compared to 3 years ago, while a negative number indicates that the school is now performing worse on these tests. In addition to this variable, there are three more variables in this data set. The first is "curriculum," which can have a value of "old" or "new," where new implies the experimental curriculum. Next is "income ($000)," which represents the average annual income (in thousands of dollars) of the households of students from each school. Finally, there is a variable called "school," which is simply ID number of the elementary school. The first step to this analysis is to generate some descriptive measures.

For each of the following points, create the chart and graph that best displays the data:

a) Show the breakdown of your sample by curriculum type (old vs. new/experimental) (2.5-points).

b) Show the distribution of the change in test scores across all schools (2.5-points).

c) Show the distribution of income across all schools (2.5-points).

Additionally, you want to generate some tables of summary statistics:

d) Create one table that calculates summary measures of the change in test scores and income variables across all 80 schools (2.5-points).

e) Create a second table that calculates summary measures of the change in test scores and income variables broken out by curriculum type (2.5-points).

Based on the graphs and tables created in parts a-e:

f) What preliminary conclusions can you draw regarding the effectiveness of the experimental curriculum (2.5-points)?

Section Three

One of the criticisms levied upon the old curriculum is that it was outdated. It was so outdated; the board members argued that it was causing standardized test scores to fall. You decide to test this hypothesis.

a) State the null and alternative hypotheses (H0 and H1) (3.75-points),

b) Test the hypothesis that the mean change in schools using the old curriculum was less than Zero (0) (3.75-points),

c) Calculate the p-value associated with the test statistic from b (3.75-points), and

d) Interpret your results (3.75-points).

Section Four

Because the school board's primary concern is whether the experimental curriculum led to better standardized test scores, the next step is to conduct a simple analysis comparing test scores from schools with the old curriculum with the test scores from schools with the new/experimental curriculum.

a) Conduct an ANOVA to evaluate whether there is a significant difference in test scores between schools with the old curriculum and schools with the new curriculum (5-points).

b) Summarize and interpret the results of your test (5-points).

Section Five

The board member who originally wanted you to include only low-income households in the survey is still concerned about the particular effect of the experimental curriculum on schools in low-income neighborhoods. To find the answer to this, you need to run a multiple regression model.

a) Create a dummy variable for the experimental curriculum and an interaction variable that interacts with the experimental dummy and the income variable (5-points).

b) Estimate a multiple regression model that includes the curriculum dummy, income, and interaction variable as independent variables (5-points).

c) Calculate predicted values for the chgtestscores variable for both the new and old curriculum for income levels of $15,000, $30,000, $60,000, and $120,000 (5-points).

d) Summarize and interpret the results of this model. What do you tell the board member about the effect of the new curriculum across different income levels (5-points)?

Section Six

Shortly after you publish the findings in a report, you receive a call from a small Midwestern school district. The schools in this district are mostly small schools in rural areas and farming communities with very low populations. They are intrigued by the findings; and want to know based on the findings, whether they might expect the same results if they adopted the experimental curriculum in their district. What do you tell them and why?

Section Seven

The variable the school board is most interested in understanding/explaining is the change in school wide standardized test scores. You were also given variables that indicated the curriculum type and the income of the households of students from each school. If this were a real research project, what other data would you collect to use as control variables? Why? In other words, what other variables would you collect that you might plausibly expect to have an impact on the change in test scores aside from income and the curriculum type?

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Solution: The downloadable solution consists of 13 pages, 2134 words and 5 charts.
Deliverable: Word Document