1
Short Answer:
15. (2 Points) List and describe all the assumptions for correlation. Pick one assumption and give an example to illustrate it.
16. (2 Points) Define the Coefficient of Determination. Use an example to illustrate the concept.
Computational (Round to TWO decimal places when necessary):
17. (2 Points) You are given the following pairs of sample scores on X (i.e., number of coins in possession) and Y (i.e., number of bills in possession). First, graph a scatterplot of the data. Make sure you label the X and Y axes properly with the correct variables. Second, describe the relationship between X and Y in one to two sentences. Third, what do you think the Pearson r will be? Do not calculate Pearson r. Based on the scatterplot, what is the approximate Pearson r (i.e., paying attention to the strength and direction)?
X Y
1 1
2 3
3 5
4 5
5 3
6 1
18. (3 Points) What is the Pearson correlation for the data below? X is SAT score and Y is GPA. Compute the correlation coefficient and interpret it (i.e., using Cohen’s guidelines). Next, test if the correlation is statistically different from zero. State the null and alternative hypotheses. Find the critical value (cv; α = .05). Calculate the t Test. State if you accept or reject the null. Lastly, describe the results in your own words. Use the Correlation activity with the step-by-step answers as a guide (i.e., posted on Blackboard).
X = SAT Y = GPA
670 3.8
450 2.9
510 2.6
530 3.4
660 4.0
19. (3 Points) A researcher is interested in determining the effect of anxiety (i.e., the IV) on statistics test scores (i.e., the DV). The researcher uses data from a sample of students drawn from KSU. The data are as follows…
Students
1 2 3 4 5
Statistics Test Score 90 60 70 90 60
Anxiety Score 3 12 7 5 8
r = -.87 = 7 = 74 sX = 3.39 sY = 15.17 sb = 1.25
First, compute and write the regression equation (i.e., remember to compute the slope and intercept and interpret each). Second, determine if the slope is statistically different from zero. Write the null and alternative hypotheses. State the cv (α = .01). Calculate the t statistic. State if you accept or reject the null. Describe the results in your own words. Calculate the CI and interpret it. Third, what would the predicted statistics test score be for a student with an anxiety score of 10? Use the Regression activity with the step-by-step answers as a guide (i.e., posted on Blackboard).
20. (2 Points) A researcher is interested in examining the impact of Facebook use on GPA. The Pearson correlation between Facebook use (i.e., the number of times a student logs in per week) and GPA is -.67. First, identify the independent variable (IV) or X and the dependent variable (DV) or Y. Second, calculate the Coefficient of Determination. Remember to interpret the effect size. Then, describe what it (i.e., the calculated Coefficient of Determination) means (i.e., the percentage/proportion of variance accounted for/explained). Use the Coefficient of Determination activity with the step-by-step answers as a guide (i.e., posted on Blackboard).
Extra Credit:
21. (1 Point) A statistician in the athletics department at the University of Michigan (UM) found a correlation between the football team’s SAT scores and undergraduate GPA to be -1.05. The UM football coach held a press conference to inform the public. He mentioned that the entire team should be congratulated and that the statistician should be praised for his/her scholarly analysis. Is the coach’s appraisal correct? Circle YES or NO. If NO, why not?
YES NO