EWU – CSBS 320 – Introductory Statistics – Briand
TakeHome-Exam 3.
Student name: ______
NOTE:
(1) The TakeHome-Exam 3 is posted on the course website, where you will be able to download an extra copy if needed (go to www.ewu.edu/econ/briand and scroll down to the CSBS 320 link).
(2) Students may work in groups, but EACH has to turn in a copy of the test.
(3) PLEASE, read carefully each question.
You will analyze students’ scores in CSBS 320. In Table 1 below, find students average scores (in percentage points) on all short-exams – CSBS 320-03 Winter 05. Students are grouped by their field of study.
Table 1.
Field of StudyCriminal Justice
Majors
(Group 1) / Business & Education
Majors
(Group 2) / Science, Math & Technology majors
(Group 3)
83
82
54
71
78
66
71
71 / 82
79
89
76
52
79
84
57 / 59
71
74
90
95
72
81
1. Explain why an ANOVA is appropriate for the situation illustrated in Table 1 above. (3 points)
2. Below compute each group mean and the grand mean. Show your work and label the different means you compute. (4 points)
3. Compute the within-groups sum of squares (SSW). Show your work – to show your work, use space available in Table 1. (4 points)
4. Compute the between-groups sum of squares (SSB). Show your work. (4 points)
5. Compute the mean square within (MSW) and the mean square between (MSB). Compute appropriate degrees of freedom (dfW and dfB). Finally compute your F-statistic (5 points)
6. To complete your ANOVA, follow steps A through D: (A) Clearly state your null hypothesis and alternative hypothesis (2 points); (B) set = 5% , look-up your critical F-value and clearly indicate what this value is (2 points); (C) compare your F-statistic to the corresponding critical F value and make a decision regarding your null hypothesis: state whether you reject or do not reject it (2 points); (D) interpret the results of your ANOVA (2 points).
7. Give the formula of the Tukey HSD statistic (1 point). If appropriate, use a Tukey HSD test to test for significant differences between pairs of field of study; show your work and interpret your results below (6 points).
Table 2 is an unorganized collection of the scores of 37 students on the PC scale; the PC scale is a Personal Control scale developed by Delroy Paulhus at the University of British Columbia which measures a person's perceived self-competence. Table 3 shows the scores of the same 37 students on take-home exam 1 in percentage points (CSBS 320-03, Winter 05).
PC scores / Exam 1 scores
8. Plot students scores on the perceived self-competence survey and on take-home exam 1 using the space below. Illustrated the PC scores on the X axis and the exam scores on the Y axis. Make sure to draw your axes, label them, and clearly indicate the scales you choose. (6 points)
9. Compute the correlation coefficient between PC scores and exam 1 scores using the conceptual formula for the correlation coefficient. To do so follow steps A through C: (A) complete the bottom of Tables 2 and 3; (B) complete table 4 and compute the standard deviations of the scores; (C) complete table 5. (6 points)
Squared Deviations / Table 5.
Z scores
PC scores (X) / Exam 1 scores (Y) / / / ZX / ZY / ZXZY
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10. Test the significance of the correlation coefficient you obtained between PC scores and scores on exam 1 for students of CSBS 320-03. Follow steps A through E: (A) clearly state your null hypothesis and your alternative hypothesis (2 points); (B) indicate how many degrees of freedom you are working with (1 point); (C) set = 5% and look-up your critical r-value in appendix I p. 310 of your textbook, clearly indicate what this value is (1 point); (D) compare your calculated value of r to your critical value of r, and make a decision regarding your null hypothesis: clearly state what that is (1 point); (E) interpret the results of your hypothesis test (2 points).
11. Give an interpretation of the correlation coefficient r your computed above (2 points).
12. Give the formula for the coefficient of determination (1 point). Compute the coefficient of determination (1 point). Give an interpretation of the value you obtained for the coefficient of determination (2 points).
13. Give the formula for the regression coefficients a and b of the regression line of Y onto X (1 point). Compute the regression coefficients a and b (2 points). Write the regression equation ( 1 point).
14. Give an interpretation of the value for the intercept of the regression equation (2 points). Give an interpretation of the value for the slope of the regression equation (2 points). Can you make any cause-and-effect statement regarding students PC scores and their scores on exam 1? (2 points)
15. Using your estimated regression equation, predict what the score on exam 1 would be for a student with a PC score of 50. ( 2 points)
16. Replicate the plot of students scores on the perceived self-competence survey and on take-home exam 1 from question 13 in the space below (2 points). Neatly draw the regression line (2 points). Clearly indicate the two points you use to draw the regression line (i.e. give me their coordinates and clearly identify them) (2 points).
17. Use a different color pen, and plot the mean scores point () on the graph above. (2 points)
Student Score: ______
Total points: 80
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