Question

Practice Exercise 24: Determining the Appropriate Analysis

For each of the following scenarios, identify the appropriate analysis. 1. The question is whether verbal reinforcement affects response rates. Subjects in Group 1 were verbally reinforced every time they respond to the instructor’s questions. Subjects in Group 2 were not. After 2 weeks, the two groups were compared by gauging the number of students who raised their hand when questions were asked. The following data were collected.

Group 1: 13, 15, 12, 17, 14, 14, Group 2: 10, 12, 12, 11, 13, 9

2. A guidance counselor at a high school wants to be best informed about the universities and colleges that students prefer most frequently. He glances at the institutions attended by last year’s graduates and notes that the three closet colleges appear to have about equal appeal. To test this assumption, he begins asking students who are planning on postsecondary schooling where they will apply. His data are as follows:

The technical institute: 22 The community college: 18 The comprehensive university: 12

3. A biology instructor wishes to know if there is a difference between performance on a state developed benchmark test and her comprehensive final examination. To maintain consistency, both test included the same number of questions (100), and the instructor used the number of items correct as the grade. The following data were collected from a sample of 10 students.

Student State exam Biology final
Student State exam Biology final
1 2 3 4 5
56 73 61 85 43
63 74 73 81 57
6 7 8 9 10
60 45 86 79 92
65 51 84 86 94

4. Assume that an educator wants to know how closely time spent doing homework is related to student grades. Data was collected from 8 students. Time spent on homework is reported in the number of hours completed per night, and grades are reported on a 4-point scale. The following data were collected.

Student	Homework	Grades	Student	Homework	Grades
1	.25	2.00	5	1.00	2.00
2	.50	1.75	6	1.25	2.25
3	.75	2.00	7	1.50	2.00
4	1.00	2.50	8	2.00	3.69

5. Three groups of students involved in the same curriculum are obliged to study for 15 minutes, 30 minutes, or 90 minutes a night for 8 weeks before taking a mathematics test. Scores from 5 students in each group were randomly selected to determine if there was a difference among the three time groups. Their scores are as follows:

15 minutes: 43, 39, 55, 56, 73

30 minutes: 55, 58, 66, 79, 82

90 minutes: 61, 66, 85, 86, 91

6. An administrator is interested in determining if the type of reading curriculum students receive is related to whether they meet reading standards for their grade. The following data were collected.

Met Standard	8	5	3
Did Not Meet	7	13	13
Standard

Answer 1

1.

Answer: Independent samples t-test

Explanation: since we are comparing two groups' mean response rates and the population standard deviation is not known, independent samples t-test will be used.

2.

Answer: One sample chi-square test

Explanation: Since we are comparing the observed proportion of students with the expected proportion, the chi-square goodness of fit test should be used.

3.

Answer: Dependent sample t-test

Explanation: Since we are doing repeated measure on same student such that the two exam scores are being measured for each students and being comapred, this is a paired sample study design.

4.

Answer: Correlation Coefficient.

Explanation: the correalation coefficient tells how well the two variables are correlated.

5.

Answer: One way ANOVA analysis

Explanation: Since we are comparing more than two group means, the one way anova analysis is used to test the hypothesis that whether there is a difference among the three group means.

6.

Answer: Chi-square test of Independence

Explanation: Since we want to test whether the two nominal variables are related or not, the chi-square test of independence should be used.