1. Characterize these correlation coefficients according to whether they are positive or negative and weak, strong, or perfect.
a. 1.00 b. -0.95 c. 0.89 d. 0.12 e. -0.11 f. 0.0 g. -1.0
2. In a data set obtained from a group of 50 individuals a correlation is obtained. If ∑ZxZy is found to be 41.3, what is the correlation between the two variables?
3. How can it be that the sum of the squared z scores =N, when man of the z scores will be very large when squared? For example, a z score of 3.0 when squared will be 9.0. Won't the sum of these scores be much larger than N? Why or why not?
4. The following data show the scores obtained by a group of students on two tests. Prepare a scatter diagram and calculate a Pearson r for these data.
|
Studen
|
Test 1(x)
|
Test 2 (y)
|
|
1
|
10
|
17
|
|
2
|
13
|
14
|
|
3
|
15
|
23
|
|
4
|
17
|
26
|
|
5
|
19
|
20
|
|
6
|
21
|
32
|
|
7
|
23
|
29
|
5. A study was conducted to examine the relationship between ratings of physical attractiveness obtained prior to and following strenuous exercise. Ten participants were given photographs to rate in terms of attractiveness. (Possible scores ranged from 1 to 25, low to high attractiveness). Following 15 minutes of aerobic exercise the same photographs (in a different order) were once again rated by subjects. The results were as follows:
|
Ratings
|
|
|
Participant
|
1st
|
2nd
|
|
1
|
13
|
17
|
|
2
|
19
|
19
|
|
3
|
9
|
16
|
|
4
|
12
|
10
|
|
5
|
16
|
18
|
|
6
|
13
|
17
|
|
7
|
12
|
14
|
|
8
|
11
|
15
|
|
9
|
10
|
12
|
|
10
|
14
|
16
|
What are you able to conclude about the relationship between the ratings obtained before and following exercise?
6. The following scores were made by 5 students on two tests. Calculate the Pearson r (using ∑zxzy/N). Convert to ranks and calculate rs.
|
Studen
|
Test x
|
Test y
|
|
1
|
5
|
1
|
|
2
|
5
|
3
|
|
3
|
5
|
5
|
|
4
|
5
|
7
|
|
5
|
5
|
9
|
7. A researcher looked at the relationship between academic achievement and average number of hours per week studying. A correlation of r = 0.5 was found. When the study was replicated the following year using students obtained from the Dean's List, and r = 0.16 was found. What might explain this variation?