1. A school teacher believes that her kindergarten students have higher IQ than average children of that age. She decided to test her hypothesis. The IQ for her class (N=30) was 106, while the population mean (μ) is 100. The standard deviation for her class was 10.
1.1. State the null and research hypothesis (H0 & H1)
1.2. Write the statistical conclusion, assuming alpha = .05 (Show your calculations).
1.3. Based on your decision to reject or fail to reject H0, what type of error can you be making? (Choose one)
Type I error
Type II error
2. A high school teacher correlated the math test scores and scores on a motivation scale for her 9th graders. She was delighted to find a high correlation between the two sets of scores. Later in the semester she correlated the math test scores of mathematically gifted students who had math scores above 85th percentile and their motivation scores. She found a much lower correlation. What could be the reason for the low correlation?
3. Suppose that a performance test of manual dexterity has been administered to three groups of subjects in different occupations. The data appear in the table below. Answer the following questions.
|
Group1
|
Group2
|
Group3
|
|
22
|
23
|
27
|
|
25
|
26
|
24
|
|
27
|
28
|
23
|
|
28
|
22
|
23
|
|
23
|
27
|
27
|
|
25
|
26
|
26
|
|
24
|
23
|
22
|
|
24
|
27
|
28
|
|
25
|
27
|
25
|
|
26
|
25
|
23
|
|
25
|
23
|
23
|
|
24
|
28
|
26
|
|
26
|
27
|
25
|
|
25
|
25
|
27
|
|
26
|
27
|
27
|
|
25
|
27
|
26
|
|
25
|
28
|
25
|
|
26
|
24
|
24
|
|
24
|
28
|
25
|
3.1. Compute the mean, mode, median, variance, and standard deviation for each group.
3.2. Graph the histograms.
3.3. Which group seems to have performed best on the test?
3.4. Which group appears to be the most homogeneous in terms of manual dexterity?
4. Thirty eighth grade students were selected from a class of a rural school. A researcher was able to obtain students' math scores in 7th grade, the teacher's evaluation scores on students' academic aptitudes in 8th grade, and students' final math scores in 8th grade. See the following table for data.
|
Math scores in 7th grade
|
Final math scores in 8th grade
|
Teacher evaluation score
|
|
75
|
43
|
4
|
|
76
|
44
|
4
|
|
68
|
36
|
1
|
|
66
|
38
|
2
|
|
73
|
41
|
2
|
|
71
|
40
|
2
|
|
55
|
27
|
1
|
|
72
|
46
|
5
|
|
61
|
38
|
2
|
|
68
|
35
|
2
|
|
64
|
31
|
2
|
|
76
|
42
|
3
|
|
71
|
45
|
4
|
|
73
|
41
|
4
|
|
78
|
45
|
5
|
|
71
|
41
|
3
|
|
86
|
50
|
5
|
|
55
|
34
|
3
|
|
96
|
51
|
4
|
|
96
|
54
|
4
|
|
50
|
28
|
2
|
|
81
|
50
|
5
|
|
58
|
37
|
3
|
|
90
|
46
|
4
|
|
58
|
23
|
3
|
|
77
|
45
|
3
|
|
88
|
55
|
5
|
|
65
|
34
|
3
|
|
77
|
54
|
3
|
|
75
|
54
|
4
|
4.1. Run a correlation analysis to examine the relationships among the three variables and interpret the results.
5. Given a normal distribution of scores with mean equal to 300 and variance equal to 100, answer the following questions.
5.1. What proportion of scores would fall below 280?
5.2. What is the probability that a randomly picked score would fall between 310 and 320?
6. A psychologist rejected the null hypothesis that there is no difference between freshmen and sophomores on drinking behavior. She used a significance level of .05 (α= .05) what is the probability of Type I error in this case?
7. Foa, Rothbaum, Riggs, and Murdock (1991) conducted a study evaluating four different types of therapy for rape victims. The Stress inoculation therapy (SIT) group received instructions on coping with stress. The Prolonged exposure (PE) group went over the events in their minds repeatedly. The Supportive counseling (SC) group was taught a general problem-solving technique. Finally, the Waiting list (WL) control group received no therapy. The data follow, where the dependent variable was the severity rating of a series of symptoms where higher scores indicate more severe symptoms.
|
Group
|
n
|
Mean
|
S.D.
|
|
SIT
|
14
|
11.07
|
3.95
|
|
PE
|
10
|
15.40
|
11.12
|
|
SC
|
11
|
18.09
|
7.13
|
|
WL
|
10
|
19.50
|
7.11
|
The below are the results from an analysis of variance.
| Descriptives |
| SYMPTOMS |
N |
Mean |
Std. Deviation |
Std. Error |
| SIT |
14 |
11.07 |
3.95 |
1.06 |
| PE |
10 |
15.4 |
11.12 |
3.52 |
| SC |
11 |
18.09 |
7.13 |
2.15 |
| WL |
10 |
19.5 |
7.11 |
2.25 |
| Total |
45 |
15.62 |
7.96 |
1.19 |
| ANOVA |
| SYMPTOMS |
Sum of Aquares |
df |
Mean Square |
F |
Sig. |
| Between Groups |
507.84 |
3 |
169.28 |
3.046 |
0.039 |
| Within Groups |
2278.738 |
41 |
55.579 |
|
|
| Total |
2786.578 |
44 |
|
|
|
7.1. What would happen to the SSgroup, the MSerror, and F if the sample sizes were twice as large as they actually were, but all other statistics remained the same?
8. Y is a measure of math achievement for students in elementary school, X1, X2, and X3 are the measures of school, class, and teacher quality, and X4, and X5 are the measures of student and parent backgrounds:
|
Y (Math)
|
X1(School)
|
X2(Class)
|
X3(Teacher Quality)
|
X4(Student)
|
X5(Parent)
|
|
7.4
|
7.6
|
5.32
|
17.2
|
2.9
|
3.43
|
|
5.3
|
5.8
|
4.88
|
-1.7
|
2.0
|
2.23
|
|
7.3
|
5.9
|
5.14
|
22.3
|
6.9
|
3.23
|
|
8.1
|
5.8
|
5.15
|
24.2
|
6.5
|
4.21
|
|
7.4
|
6.1
|
5.88
|
16.3
|
3.0
|
5.21
|
|
6.7
|
4.1
|
4.32
|
16.2
|
4.5
|
4.32
|
|
8.3
|
5.0
|
4.98
|
22.7
|
7.7
|
4.65
|
|
6.7
|
4.9
|
5.00
|
9.8
|
2.5
|
4.23
|
|
8.2
|
6.2
|
5.32
|
19.9
|
6.5
|
5.65
|
|
7.4
|
4.8
|
5.60
|
10.0
|
1.0
|
4.43
|
|
4.6
|
4.2
|
4.70
|
-2.9
|
1.2
|
2.43
|
|
7.0
|
5.0
|
4.72
|
10.9
|
2.2
|
4.43
|
|
6.9
|
4.4
|
4.90
|
14.8
|
1.4
|
4.21
|
|
6.6
|
5.3
|
5.16
|
9.0
|
3.2
|
4.45
|
|
4.5
|
5.4
|
5.04
|
-6.1
|
1.2
|
3.54
|
|
7.9
|
6.3
|
5.01
|
20.6
|
6.8
|
5.65
|
|
6.4
|
7.1
|
4.96
|
12.7
|
4.2
|
4.54
|
|
6.3
|
5.0
|
5.11
|
-1.1
|
1.7
|
4.65
|
|
8.6
|
5.4
|
5.11
|
25.1
|
8.6
|
6.50
|
|
8.2
|
4.7
|
5.10
|
22.8
|
7.7
|
6.25
|
8.1. Do the school, class, and teacher measures contribute to the predictability of Y?(1 POINT) What is the equation? (1 POINT)Report your results with interpretation.
8.2. Do the student and parent measures contribute to the predictability of Y? (1 POINT)What is the equation? (1 POINT)Report your results with interpretation.
8.3 Do the student and parent measures contribute to the predictability of Y beyond that which is predicted by the school, class, and teacher measures? How do you know?
9. As shown in the table below, subjects were randomly assigned to three groups in an experimental study. Group A received large amounts of praise, Group B received moderate amounts of praise, and Group C received no praise for correct answers to math problems. Their scores on an exam are shown in the table.
|
Group A
|
Group B
|
Group C
|
|
7
6
5
8
3
7
|
4
6
4
7
5
7
|
3
2
1
3
4
1
|
9.1. Is there evidence that the scores from the three groups showed an overall significant difference? If so, what is the effect size?
9.2. If you need further steps to identify which group(s) is (are) different from each other, please choose an appropriate method to do so and report and interpret the results.
10. The Thematic Apperception Test presents subjects with ambiguous pictures and asks them to tell a story about them. These stories can be stored in any number of ways. The researchers asked mothers of 15 normal and 15 schizophrenic children to complete the TAT, and scored for the number of stories (out of 10) that exhibited a positive parent-child relationship. The data follow:
Normal: 8 4 6 4 3 1 4 4 6 4 2 2 6 3 4
Schizophrenic: 2 1 1 3 2 7 2 1 3 1 0 2 4 2 7
10.1. State the null and research hypothesis (H0 & H1)
10.2. Is therea significant difference between the normal and the schizophrenic groups in positive mother-child relationship.If so, what is the direction and effect size of the difference?
11. In a study of 682 college students, respondents were asked whether or not they had been unfaithful in the context of a romantic relationship. 103 out of the 480 female respondents indicated that they had been unfaithful and 53 out of the 202 male respondents indicated that they had been unfaithful. Is there a statistically significant difference between males' and females' tendency toward relationship infidelity? If so, what is the direction and effect size of the difference?