Statistics Review Problem Set

1. The following is a hypothetical set of anxiety scale scores from a population of students being seen at a college counseling center:

5 16 47
6 18 50
9 25 50
10 46 50
12 47 78

What are the Z and the T scores of the person who scored 6? 18? Of the two people who scored 47? Of the person who scored 78? Why is it not a good idea to use Appendix C to compute percentiles for these scores?

2. SAT scores are normally distributed, with a mean of 500 and sd of 100. Find the Z, T, and percentile equivalents of the following scores: 500, 510, 450, 460, 650, and 660.

3. Jack, Jill, James, and John all took a math aptitude test. The test was normed on a group that had a mean score of 70, s = 15; the scores were normally distributed. Complete the following table.

4. Draw a diagram that shows the relationship of a raw score of 20 to Z, T, and percentile in a distribution with the following:

(a) M = 20, s = 5
(b) M = 40, s = 7
(c) M = 15, s = 4
(d) M = 25, s = 10

1. Given the following N's (where N is the number of pairs of observations) and obtained r's, indicate whether the result is significant at the .05 level:

(a) N = 100, r = .22
(b) N = 100, r = .60
(c) N = 9, r = -.70
(d) N = 36, r = .23
(e) N = 100, r = -.19

2. Given the following data, what are the correlation and the coefficient of determination between:
(a) IQ scores and anxiety test scores?
(b) IQ scores and statistics exam scores?
(c) Anxiety test scores and statistics exam scores?

Indicate whether the obtained r is statistically significant, and, if so, at what level. Also, would you consider the magnitude of the relationship large enough to be useful in making predictions about student achievement?

3. Here's another set of measurements; again, find the value of r, whether that value is significant at the .05 level, and the coefficient of determination for each possible pair.