Project 2: Part 1

NOTE:  Discussion is allowed but each person is expected to write their own, using resources and information from class, the library etc.

Question 1: (18 points)

There are 10 students in a classroom. The following table shows students’ names, their final scores, and two items of the final test (Items 1 and 2). Use this dataset to summarize students’ performance and to conduct an item analysis.

Regarding summarizing test scores:

1. Given the dataset above, compute the following statistics: Range, Mean, Mode, Median, Variance, and Standard Deviation? (6 points)

2. Decide whether the shape of the distribution is symmetrical, positively skewed, or negatively skewed (explain how your decision is made and provide statistical evidence, such as mean, median, and mode) and use the shape of distribution to describe how students perform on their final exam. (2 points)

Regarding conducting item analysis:

3. Given the dataset above, compute the difficulty (p) and discrimination index (D) for Items 1 and 2 (Construct a table for high and low performing groups and show all your computational processes in details). (6 points)

4. Provide a short explanation about what these results are telling you regarding items 1 and 2 (i.e., use these statistical item properties, such as item difficulty and discrimination, to explain the quality of Items 1 and 2). (4 points)

To answer the next set of questions in #2, you will need to carefully study the Power Point on the Normal Curve and Standardized Scores. Be sure to view the notes that go with each slide in the Power Point presentation as the notes provide information that is essential to understanding the slides. Your text also has very helpful information in Chapter 14. Here are a few resources I have compiled to help jog your memory.

Z-score formula:

Z = (X –M)/SD

For example, a student score on the GRE quantitative exam (X) minus the mean on the GRE quantitative (M). Divide that difference by the standard deviation (SD)

(see pages 273-276 in your book, 11^th edition)

T-score formula:

T = 10z + 50

Multiply the z-score (z) by 10 and add 50 to this value to obtain the equivalent T-score (T).

(see page 277 in your book, 11^th edition)

Question 2: (26 points)

The National Center for Educational Statistics report that in the year ending 2009 400,000 students took the Graduate Record Examination (GRE). For this set of examinees, the observed mean Verbal score was 560 with a standard deviation (SD) of 90, and the observed mean Quantitative score was 490 with a standard deviation (SD) of 100.

Assuming that the distribution of scores on the 2009 GRE was normal, answer the following questions regarding both tests (Verbal and Quantitative): (Show all your computations and use statistical evidence to interpret your answer). Number your responses and circle your final answers.

(1 point for each item from 1-4)

Note: please notice that one of these questions ask for a percent and the others ask for the number of students. Respond appropriately.

1. What percent of student scores were below the mean?
2. How many student scores were above the mean?
3. How many student scores fall between 1 SD below the mean (-1SD) and 1 SD above the mean (+1SD).
4. How many students scores were higher than 2 SD above the mean.

(2 point for each item from 5-14)

5. Ann has a score of 380 on the Verbal exam. What is her z-score?
6. What is Ann’s percentile rank?
7. How was Ann performing relative to her peers?
8. What is the z-score of Sam who scores 760 on the Quantitative exam?
9. What is Sam’s percentile rank?
10. How was Sam performing relative to his peers?
11. Betty’s score on the Verbal exam is 1 SD above the mean. What is her score?
12. John scores 500 on the Verbal exam. What is his z-score?
13. Convert John’s score above to a T-score.
14. If Nicole had a Quantitative score of +1.5 SD’s what was her raw (numerical) score?
15. If a student had to score at or above the 84^th percentile for both tests to be considered for a full scholarship at USF, what would be the minimum score needed on Verbal and Quantitative exams?

Question 3: (6 points)

You have a student, Tej, entering your school from India. You need to know which math class you should place him in. The scores you normally use are SAT scores (mean=500 and standard deviation=100). The rules you use for placement are:

700-800 Calculus
500-699 Trigonometry
300-499 Geometry
100-299 Algebra

However, this student did not take the SAT, but instead took the AAT (Academic Aptitude and Achievement Test). Scores for the AAT are reported with a mean of 80 and a standard deviation of 4. Tej received a raw score of 92 on the math portion of the AAT. Convert his scores to a metric so that they are comparable to SAT scores, then decide in which math class Tej should be placed. (Hint: you could begin by converting his AAT to a z-score).

Your answer should include at least 2 paragraphs:

1. Explain (using words and numbers) which course Tej should be placed in, and why. Make sure to include a thorough explanation. (5 points)
2. Find and provide some background information on the AAT and include an explanation of why this might be an appropriate score to use for this purpose. Include the reference you used for information on the AAT. (1 point)