# Part I A researcher was interested in comparing three methods of d...

## Question

Part I
A researcher was interested in comparing three methods of dropout prevention in at-risk high school students: a structured work-study program, a peer-buddy program, and teacher
mentoring program. Thirty at-risk students were randomly assigned to each of these three treatments at the beginning of their sophomore year. At the end of the year, the researcher noted how many students were still enrolled in school and how many appeared to have dropped out.
These are the data that were obtained:

End of Year Status
Program    Still Enrolled    Not Enrolled
Work-Study       11                   19
Peer Buddy       16                   14
Teacher Mentor 20                   10

1. State the null hypothesis of interest in this study.
2. Conduct an appropriate test of this null hypothesis, using an alpha level of .05. These can be calculated using SAS (Syntax and outputs should be attached).
3. Write a one-paragraph interpretation of the results of this research.
4. Calculate the effect size associated with these data.
5. Estimate the power of the hypothesis test.

Part II.
A researcher was interested in college students' attitudes towards alcohol consumption, and was intrigued by previous research (e.g., Wobble, 2000) that indicated a lack of significant differences between students enrolled in different colleges. The researcher has hypothesized that these results are attributable to confounding effects of gender, a variable that was not controlled in previous studies. For a new investigation, the researcher drew six samples of students, a sample of male students and a sample of female students from each of three colleges: the College of Business Administration, the College of Fine Arts, and the College of Arts and Sciences. She made certain that all students in the samples were seniors and that all were enrolled full-time in their respective programs. Each student completed the Attitude Toward Alcohol Scale (Tipsey & Stumble, 1977) which yields scores ranging from 50 to 120, with higher scores representing a greater propensity towards alcohol consumption. These are the resulting data:

College
Gender            Business          Fine Arts            Arts and Sciences
Female                   83                   78                              86
91                   94                              78
76                   89                              72
72                   82                               69
88                   87                               81

Male                      91                   88                               96
97                   104                              87
83                   99                               83
79                   92                               79
95                   97                               91

6. State the null hypotheses that should be tested in this study.
7. (a) Identify the independent variables and the dependent variable in this study? (b) For the independent variables, are they categorical or continuous variables? (c) For the dependent variable, is it a categorical or continuous variable? If the independent or dependent variable is a categorical variable, how many levels is it?
8. Conduct an appropriate test of each null hypothesis, using an alpha level of .05. These can be calculated using SAS (Syntax and outputs should be attached).
9. Construct the table including cell means, marginal means, and the grand mean.
10. Sketch a graph of the cell means obtained in this research.
11. Construct an ANOVA summary table that could be used to communicate the results of these statistical hypothesis tests.
12. Conduct multiple comparisons (as needed),
13. Calculate the sample estimates of the following elements of the linear model for these data:
Ẍ...
α1, α2
β1, β2, β3
αβ11, αβ13, αβ22, αβ23
ε211, ε312, ε513, ε421, ε222, ε123

14. Calculate the effect size associated with the gender main effect.
15. Estimate the statistical power of the F test for the gender main effect.
16. Write a one-paragraph interpretation of the results of this research.

Part II
A researcher was interested in the influence of test administration practices (in-class testing vs. take-home testing) on student anxiety. A volunteer sample of 18 undergraduate psychology students participated. The students were pretested with a trait anxiety instrument, and on the basis of their scores, were classified as High Anxious or Low Anxious. Students within each anxiety category were then randomly assigned to receive either a take-home midterm examination or an in-class midterm examination. The researcher hypothesized that the ‘impact’ of test type would be greatest for the high anxiety students. On the day of the examination, the researcher administered a test anxiety instrument to obtain a measure of the students’ anxiety about taking the midterm. The following test anxiety scores were obtained:
Type of Test
Student Trait Anxiety       In-Class      Take-home

Low                                       22                16
21                17
20                18
22

High                                     21                  35
33                   25
25                   28
24                   23
19                   21
22

17. State each null hypothesis tested in the ANOVA.
18. Conduct the analysis using all three approaches described in the Articulate presentation (experimental, regression, and hierarchical), using both possible hierarchies for the latter analysis. These can be calculated using SAS (Syntax and outputs should be attached).
19. Sketch a graph of the cell means obtained in this research.
20. Write a one-paragraph interpretation of the results of this research.

## Solution Preview

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1. State the null hypothesis of interest in this study.

H0: The variable program (Work-Study/Peer Buddy/Teacher Mentor) and the variable end of year status (Still Enrolled/Not Enrolled) are independent
H1: The variable program (Work-Study/Peer Buddy/Teacher Mentor) and the variable end of year status (Still Enrolled/Not Enrolled) are not independent

2. Conduct an appropriate test of this null hypothesis, using an alpha level of .05.These can be calculated using SAS (Syntax and outputs should be attached).

Code and output attached

3. Write a one-paragraph interpretation of the results of this research.

From the results, we can see that the p-value (2(2) = 5.43, p = 0.0661) is not less than the level of the significance i.e. 0.05 therefore, we will not reject the null hypothesis and will conclude that “The variable program (Work-Study/Peer Buddy/Teacher Mentor) and the variable end of year status (Still Enrolled/Not Enrolled) are independent”. Furthermore, we can see that the effect size (w) is 0.4144 and the value of Cramer’s V is negative of w, value 0.2457 suggests the effect size is medium to large....

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