question archive Items 7 through 11 refer to the admission procedure for Watsamata University, a small private University in Minnesota
Items 7 through 11 refer to the admission procedure for Watsamata University, a small private University in Minnesota
Subject:StatisticsPrice: Bought3
Items 7 through 11 refer to the admission procedure for Watsamata University, a small private University in Minnesota. Watsamata University requires all applicants to submit a admission examination specifically developed for the University. The test is composed of 100 multiple-choice items. To evaluate the utility of test for admission decisions the university conducted a pilot study in which, for one year, all students who were admitted to the university took the test. The descriptive statistics from the study are presented in Table 1. The relationship between scores on the admission test and freshman year GPA is displayed in the scatter plot shown in Figure 1.
Table 1. Descriptive statistics for admission test evaluation study. N = 50
Admission Tests Scores
Freshman GPA
Mean
57.0
2.55
Standard Deviation
14.3
0.765
Figure 1. Scatter Plot admission test scores with freshman year Grade Point Average (GPA), r = 0.85
7. Using the available data, what is the reliability of this data. (5 points)
The reliability of this data is reported in the scatter plot as 0.85. Normally, perfect reliability is a 1.0 (range of -1 to +1), so the relationship between admission test scores and freshman year GPA is high.
8. Using your response to item seven, what would you expect the reliability of the data to be if the number of test items were increased to 150? (5 points)
Test reliability increases as one adds test items, as long as the number of test items makes the test so long that test takers become fatigued. This addresses the concern of content sampling error.
9. Construct a regression formula for this test and freshman GPA, and use it to calculate the predicted freshman year GPA for the student who scored 63 on the admissions examination. What range of scores would you predict, with 90% confidence, for this student's first year GPA? (10 points)
10. The admissions department assumes that subsequent classes will exhibit the same pattern of performance on the admission test, and that the relationship between the admissions examination and the students' freshman GPA is relatively stable. Watsamata University has a very simple admission procedure. If a student scores 60 or better on the admission examination, he or she is accepted. In addition students must maintain a 2.0 GPA to continue their studies at Watsamata University. Given this information, is the use of the test likely to enhance the validity of admission decisions made by Watsamata University? Justify your answer using the concepts discussed in class. (10 points)
11. Watsamata University is investigating whether or not its admission test exhibits gender bias. They used the data from the pilot group. The descriptive statistics for male and female applicants, as well as the respective correlation coefficients appear Table 2.
