1. Kayla, a preschooler, is given a 20-item test to assess her early literacy skills. In this test, she is asked to indicate whether not two words begin with the same sound (e.g., "boy" and "ball").
a. If Kayla were simply guessing at the answers, how many items would we expect that she would correctly answer?
b. If Kayla were guessing at the answers, and based on the binomial formula (see lecture notes), compute the probability that the Kayla would correctly answer...
a. exactly 13 items
b. more than 14 items (i.e., 16 or more items correct.)
c. more than 14 items or less than 6 items
You may compute these probabilities using the binomial formula, or using an online binomial calculator such as those available here or here.
Below are the actual results of Kayla's test. Note that for the "response" variable, 0 = incorrect and 1 = correct.
|
Item
|
Response
|
|
1
|
0
|
|
2
|
1
|
|
3
|
1
|
|
4
|
0
|
|
5
|
1
|
|
6
|
1
|
|
7
|
1
|
|
8
|
1
|
|
9
|
1
|
|
10
|
0
|
|
11
|
0
|
|
12
|
1
|
|
13
|
1
|
|
14
|
1
|
|
15
|
0
|
|
16
|
1
|
|
17
|
1
|
|
18
|
1
|
|
19
|
1
|
|
20
|
1
|
c. How many correct responses does Kayla actually have?
d. Has Kayla performed at a level that is significantly better than chance (i.e., guessing)? Carry out a binomial test using SAS or SPSS. Use as the criterion of significance. Show all four steps of your hypothesis test: (1) null and alternative hypotheses, (2) specified alpha level, (3) test statistic and p-value, and (4) decision.It will be helpful to paste in the relevant SAS or SPSS output.
The following exercise is taken from Howell (1989).
2. McConaughy (1980) has argued that younger children organize stories in terms of simple descriptive ("and then...") models, whereas older children incorporate causal statements and social inferences. Suppose that we ask two groups of children differing in age to summarize a story they just read. We then count the number of statements in the summary that can be classified as inferences. The data are as follows:
|
Number of inferences
|
Child's
Status
|
|
0
|
Younger
|
|
1
|
Younger
|
|
0
|
Younger
|
|
3
|
Younger
|
|
2
|
Younger
|
|
5
|
Younger
|
|
2
|
Younger
|
|
4
|
Older
|
|
7
|
Older
|
|
6
|
Older
|
|
4
|
Older
|
|
8
|
Older
|
a. Do older children differ from younger children in the number of inferences they make? Assess this using the Mann-Whitney test using either SAS or SPSS (or both, if you wish). Use as the criterion for significance. Show all four steps of your hypothesis test: (1) null and alternative hypotheses, (2) specified alpha level, (3) test statistic and p-value, and (4) decision.
4. A psychologist operating a group home for troubled adolescents wants to compare the effectiveness of this setting to that of foster homes and natural homes. She samples n = 9 adolescents from each setting and has a second psychologist interview each adolescent, and rates her or his well-being on a scale from 1-20. Below are the ratings (note. 1 = natural home, 2 = foster home, 3 = group home):
|
Rating
|
Setting
|
|
15
|
1
|
|
18
|
1
|
|
19
|
1
|
|
14
|
1
|
|
5
|
1
|
|
8
|
1
|
|
12
|
1
|
|
13
|
1
|
|
7
|
1
|
|
16
|
2
|
|
14
|
2
|
|
20
|
2
|
|
22
|
2
|
|
19
|
2
|
|
5
|
2
|
|
17
|
2
|
|
18
|
2
|
|
12
|
2
|
|
10
|
3
|
|
13
|
3
|
|
14
|
3
|
|
11
|
3
|
|
7
|
3
|
|
3
|
3
|
|
4
|
3
|
|
18
|
3
|
|
2
|
3
|
a. Is the setting of adolescents related to their well-being? Assess this using the Kruskal Wallis test using SPSS or SAS. Use . Show all four steps of your hypothesis test: (1) null and alternative hypotheses, (2) specified alpha level, (3) test statistic and p-value, and (4) decision.
b. If an overall difference exists, carry out post-hoc tests to assess particular pairwise differences (use an overall ).Remember to adjust the pairwise alpha level.
5. In a study of engaged couples' preferences with respect to size of family, n = 26 engaged couples were selected at random and were asked to state, independently, the ideal number of children each would like to have. Responses of each man and woman are listed below:
|
Couple ID
|
Man
|
Woman
|
|
1
|
3
|
2
|
|
2
|
0
|
1
|
|
3
|
1
|
0
|
|
4
|
2
|
2
|
|
5
|
0
|
3
|
|
6
|
2
|
3
|
|
7
|
1
|
2
|
|
8
|
2
|
3
|
|
9
|
2
|
3
|
|
10
|
1
|
3
|
|
11
|
2
|
4
|
|
12
|
0
|
1
|
|
13
|
3
|
4
|
|
14
|
5
|
2
|
|
15
|
7
|
2
|
|
16
|
1
|
2
|
|
17
|
0
|
3
|
|
18
|
2
|
4
|
|
19
|
0
|
3
|
|
20
|
2
|
3
|
|
21
|
2
|
4
|
|
22
|
0
|
2
|
|
23
|
1
|
3
|
|
24
|
3
|
2
|
|
25
|
5
|
2
|
|
26
|
0
|
1
|
a. Carry out a Wilcoxon matched-pairs test (using SPSS) to assess whether men and women differ in their view of ideal number of children. Use . Show all four steps of your hypothesis test: (1) null and alternative hypotheses, (2) specified alpha level, (3) test statistic and p-value, and (4) decision.
6. Fifteen political scientists ranked each of three countries ("A," "B," and "C") in terms of the perceived "political responsibility" each manifests. The data (rank of each country by each rater) are indicated below:
|
|
Country
|
|
Rater
|
A
|
B
|
C
|
|
1
|
5
|
5
|
6
|
|
2
|
11
|
11
|
9
|
|
3
|
6
|
8
|
5
|
|
4
|
12
|
14
|
11
|
|
5
|
8
|
6
|
6
|
|
6
|
5
|
8
|
6
|
|
7
|
7
|
7
|
5
|
|
8
|
5
|
8
|
4
|
|
9
|
12
|
14
|
9
|
|
10
|
8
|
8
|
4
|
|
11
|
5
|
8
|
4
|
|
12
|
6
|
8
|
5
|
|
13
|
7
|
7
|
8
|
|
14
|
6
|
7
|
7
|
|
15
|
7
|
9
|
13
|
a. Use Friedman's test to assess whether the countries differ in perceived political responsibility(using SPSS). Use .Show all four steps of your hypothesis test: (1) null and alternative hypotheses, (2) specified alpha level, (3) test statistic and p-value, and (4) decision.
b. Which specific pairs of countries differ from one another? Assess this by using Wilcoxon matched-pairs tests as a post hoc procedure (using SPSS). Use an overall . Remember to adjust the alpha level used for each pairwise comparison.