POL251_HW7

POL 251: Introduction to Political Science Methods Homework #7 Due Thursday, November 30 @ 2:30pm (upload to the BlackBoard assignment, write all partner names on document) Question 1: A researcher wants to know if there is a strong positive correlation between University of Mississippi students' ACT scores and their first year GPA. She asked 15 sophomores at random for their freshman year GPA and their ACT scores, and got the following values: Freshman Year GPA (y) ACT Score (x) xy y 2 x 2 2.3 27 3.3 33 3.1 28 3.7 31 2.8 22 3.0 31 3.9 33 2.6 26 3.3 30 3.5 29 2.9 25 3.4 32 2.1 20 2.7 23 3.8 34  =  =  =  =  = (Note: These values are not actual Ole Miss students’ GPAs and ACT scores) (1) Complete the table above with the appropriate values to calculate Pearson’s correlation coefficient (r). (2) Calculate Pearson’s correlation coefficient (r) for the relationship between ACT scores and freshman year GPAs. Use the formula and the "Correlation Steps" document. Show all of your work, and round to 2 decimal places. (3) Based on Pearson’s r, how would you describe the relationship between ACT scores and freshman year GPAs (ex: weak negative, no relationship, etc.)?

(4) Calculate the correct t statistic for this Pearson’s r. Show all of your work, and round to 2 decimal places. Use the formula provided in the "Correlation Steps" document. (5) What degrees of freedom do you need to use for this statistical test? Show all of your work. (6) Do you need to use a one-tailed or a two-tailed test for this statistical comparison? (Hint: Go back and read the proposed relationship stated in the introduction of this question. Is it directional or non-directional?) (7) Using the t lookup table, what is the critical test statistic value that coincides with α = 0.05, the appropriate tailed test, and the appropriate degrees of freedom? (8) Determine whether ACT scores have a strong positive correlation with first year college GPAs, is this relationship significant at α = 0.05, and state why.