Reference no: EM133194723

Assignment: Null and Alternative Hypotheses Exam

Directions:

The purpose of this assignment is to test your ability to appropriately apply and interpret the statistical techniques learned in class. The application of the techniques depends on the research question and the structure of the data. To this end, your job is to (i) fully comprehend the research question/issue presented in the scenario (ii) appropriately identify the level of measurement for each variable (iii) use the correct methodological technique and (iv) and adequately interpret the results. Each answer MUST include the following:

A. The research question at hand

B. The null and alternative hypotheses

C. The variables used (clearly identified the IV(s) and DV)

D. The appropriate test to answer the research question based on the structure of the data.

E. The appropriate outputs. Only include relevant outputs!

F. A full interpretation of the results. This includes both the descriptive statistics, an interpretation of the inferential statistics, and your conclusion of the research questions based on the results. When interpreting the results you should discuss your findings as if you were communicating with someone who does not have a statistical background. Note, students looking for "value added" points will go beyond simply determining if a significant relationship exists and discuss the substantive meaning of the results.

General Background:

The Farfromperfect School District is looking for ways to improve student test scores due to recent changes in the state funding scheme. The state has long tied funding to student performance on standardized testing. Over the years, research has shown that while teacher quality does impact test scores, a strong predictor of success on the state's standardized test is socio-economic background (SES). On average, schools with more low-income students have lower overall test scores than schools with fewer low-income students. As a way to provide low-income students with adequate academic support, the state has devised a new scheme to reward schools for advancing low-income student achievement on the test.

The Farfromperfect School District has a large number of students that come from lower SES households, and is experimenting with a variety of programs and ideas in hopes of increasing low-income student test scores. The Farfromperfect School District has hired you to help them understand if their efforts will pay off at test time, and to gain insights on a variety of other questions. Luckily for you, the District has collected data that you believe will be useful. First, the District uses a practice test designed to mimic the material on the State standardized test as a way to track progress. Students take the practice test at the beginning of the school year and at the conclusion of the Fall semester. The test covers reading, math, and science. The District also collects student demographic information, parent demographic information, information on program initiatives, and extracurricular activities. They have separated their dataset to include only students who receive free or reduced lunch (their proxy measure for SES) and supplied you with a dataset containing variables related to several questions they would like answered.

Task

The District has spent considerable effort to improve their math test scores, and they are interested to know if their practice scores differ from the current state benchmark. Each student took the practice test at the beginning of the year and was given the test again at the end of the semester. The variables ASMath1 contain data for the test taken by students at the beginning of the year. ASMath2 contain data on scores taken later in the school year.

Question I: Is there a significant difference between the practice test scores of low income students and the state math benchmark of 14.6?

In addition to knowing how close to the state benchmark the District is, they are also interested in knowing how students have progressed in their math comprehension over the semester. As noted above, the District uses a pre/post test model to track progression over the semester.

Question II: Have math test scores significantly improved from the beginning of the year?

Because the Farfromperfect School District is really concerned with improving tests scores of their low-income students, the school district would like to consider potential cultural and gender differences that may influence testing and test preparation. For example, some research shows that female students sometimes do not put forth full effort because they fear "being made fun of" by other students. There is also a cultural bias that steers females away from math and science because of the apparent belief that these are male dominated subjects. Additionally, the Farfromperfect School District has a high Hispanic population and language barriers may inhibit performance on the test. In sum. the Farfromperfect School District wants to identify patterns related to race and gender so that they may alter their efforts to accommodate the needs of their students and combat issues noted in the literature. (Hint: You will need to consider which math test score to use for this question as one of the scores is better suited to answer the questions below).

Question III: Do gender differences exist in math scores?

Question IV: Do differences exist in math scores between racial categories?

Guided by research that shows math grades can be improved through additional independent study time and individualized instruction outside of the classroom, the Farfromperfect School District has engaged in two programs in hopes of increasing math grades. The first is an incentive program where students who spend at least five hours a week at home working on math are rewarded with an end of the semester party. The other program uses Education majors from a nearby university to provide math tutoring during enrichment periods (aka-study hall).

Question V: The District would like to know how participating in these programs correlates math scores. Would you recommend the District continue with the programs? Would you recommend the District put more resources in one program over the other? Be sure to justify your conclusions based on the outputs.

Question VI: How does increasing the number of hours studying math home influence a student's math score? What math score would we expect to see if a student studied 1 hour per week? Compare this to a student who studies 5 hours per week and a student who studies 10 hours per week.

Question VII: How does the number of tutoring sessions attended influence a student's math score? What math score would we expect to see if a student studied 5 tutoring sessions? Compare this to a student who attends 10 sessions. What recommendations would you make based on your findings?