You have a student, Martina, entering your school from another state. You need to know which math class you should place her in. The scores you normally use are SAT scores (mean=500 and standard deviation=100).
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: (22 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 item analysis. (Show all your computation and use statistical evidence to interpret your answer)
Student Name
Final Score
Item 1
Item 2
Casie
87
Correct
Correct
Jeremy
70
Incorrect
Incorrect
Travis
90
Correct
Correct
Tomeka
85
Correct
Correct
Tony
60
Correct
Incorrect
Sing-Hie
75
Correct
Incorrect
Ricardo
87
Correct
Correct
Mary Lou
92
Correct
Incorrect
Terry
64
Correct
Incorrect
Wanda
80
Correct
Incorrect
Regarding summarizing test scores:
1. Given the dataset above, compute the following statistics: Range, Mean, Mode, Median, Variance, and Standard Deviation (Show all your computation and/or interpret how you obtain your answers)? (6 points)
2. (a) 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 (b) use the shape of distribution to describe how students perform on their final exam. (4 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). (8 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)
Question 2: (22 points)
The National Center for Educational Statistics report that in the year ending 2009 some 400,000 students took the Graduate Record Examination. For this set of examinees, the observed mean Verbal score was 490 with a standard deviation (SD) of 90, and the observed mean Quantitative score was 560 with a standard deviation (SD) of 100.
Assuming the distribution was normal, answer the following questions regarding both tests: (Show all your computation and use statistical evidence to interpret your answer)
(1 point for each item from 1-4)
1. How many students whose scores are below the mean scores.
2. How many students whose scores are above the mean scores.
3. How many students whose scores fall between 1 SD below the mean (-1SD) and 1 SD above the mean (+1SD).
4. How many students whose scores are higher than 2 SD above the mean.
(2 point for each item from 5-13)
5. Ann has a score of 670 in the Verbal exam. What is her percentile rank?
6. How was Ann performing relative to her peers?
7. What is the percentile rank of Sam who scores 460 in the Quantitative exam?
8. How was Sam performing relative to her peers?
9. Betty’s score in the Quantitative exam is 1 SD above the mean. What is her score?
10. John scores 500 in the Quantitative exam. What is his Z score?
11. Convert John’s score above to a T-score.
12. If Nicole had a Verbal score of +1.5 SD’s what was her raw score?
13. If a student had to score at or above the 84th 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, Martina, entering your school from another state. You need to know which math class you should place her 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. Scores for the AAT are reported with a mean of 80 and a standard deviation of 8. Martina received a raw score of 84 on the math portion of the AAT. Convert her scores to a metric so that they are comparable to SAT scores, then decide in which math class Martina should be placed.
In one or two paragraphs, explain (using words and numbers) which course Martina should be placed in, and why. Make sure to include all your computation and a thorough explanation along with any appropriate references.
