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.

Question 3: It is common to think of midterm elections as a referendum on the sitting president. Below is a screenshot of CNN's 2022 election exit poll that sampled voters across the United States and asked them which party's candidate they voted for in their district's House race. Based on this graph, I have created the table below that breaks down vote choice by approval of President Biden. This table has N=1830. I am hypothesizing that there is a significant relationship between Biden approval and party vote choice. (1) Fill in the table above with the expected frequencies for each cell. Show your work, and round your answers to whole numbers . Strongly Approve Somewhat Approve Somewhat Disapprove Strongly Disapprove Total Voted for Democrat in House race Observed frequency (f 0 ) 319 438 94 42 893 Expected frequency (f e ) f 0 - f e (f 0 - f e ) 2 (f 0 - f e ) 2 / f e Voted for Republican in House race Observed frequency (f 0 ) 13 43 91 790 937 Expected frequency (f e ) f 0 - f e (f 0 - f e ) 2 (f 0 - f e ) 2 / f e Total 332 481 185 832 1830

(2) Conceptually , what do these expected frequency values represent in this case? State your answer in a couple words. (3) Fill in the table above with the following: f 0 - f e , (f 0 - f e ) 2 , and (f 0 - f e ) 2 / f e. . Show all of your work. Please round all values to 2 decimal places . (4) Calculate the chi-square for this table. Show all work and round your answer to 2 decimal places . (5) What degrees of freedom do you need to use for this statistical test? Remember: degrees of freedom = (number of rows – 1)*(number of columns – 1). Show all of your work. (6) Find and write down the critical value of chi-square at α = 0.05 using the Chi-Square lookup table. (7) Should the researcher reject the null hypothesis in this case? In other words, is there a significant relationship between Biden approval and party vote choice at α = 0.05? Explain why or why not.