1. Politics & You R. Stephens Introduction to Statistics November 13, 2015

2. Goals Investigate any relationships and/or differences between: Political parties and SATs Political parties and GPAs Degree of Conservatism and GPAs

3. Background Information Personal anecdotal evidence Other studies done?

4. Methods Respondents: 116 Intro to Stats students from fall of 2008 Gathered answers to: Colgate GPA Math & Verbal SAT Political party Degree of Conservatism (DOC)

5. Basic Political Statistics Number of Democrats: 42 Number of Republicans: 33 Democrats: 1300 Average SAT with SD of 122.10 Republicans: 1351.8 Average SAT with SD of 101.96 Democrats: 3.1738 Average GPA with SD of.3652 Republicans: 3.1212 Average GPA with SD of.3666

6. Hypothesis Testing We perform two separate 2-sample z- tests for Democrats versus Republicans: H 0 : Same SAT versus H A : Rep. have higher SAT H 0 : Same GPA versus H A : Dem. have higher gpa We will set the significance level at 5%.

7. H 0 : Same SAT versus H A : Rep. have higher SAT Observed difference: 51.8 Se avg for Dem: CF (122.10) / √42= 18.763 Se avg for Rep: CF (101.96) / √33 = 17.647 Se diff = √(18.763 2 + 17.647 2 ) = 25.758 Z = (51.8 - 0)/25.758 = 2.01 P-value of 2% Reject H 0 and conclude that Republicans have higher sat scores. We assume a colgate population of 2800 in our calculations of cf = √[(2800 - sample size)/2799]

8. H 0 : Same GPA versus H A : Dem. have higher GPA Observed difference:.0526 Se avg for Dem: CF (.3652) / √42 =.05594 Se avg for Rep: CF (.3666) / √33 =.06345 Se diff = √(.05594 2 +.06345 2 ) =.08459 Z = (.0526 - 0)/.08459 =.62 P-value of 27% Not enough evidence to be able to reject H 0. not a significant difference in GPAs.

9. Are GPA and Degree of Conservatism related? 1 - 9 scale; 1 being most liberal Deleting those who did not respond, we have 111 data points. Using excel’s CORREL function, r = -.0528 Between gpa and DOC. Using the hypothesis test for correlation, H 0 : ρ =0 versus H A : ρ<0, we find z 109 = (-.0528) √109 = -.55 p-value of 29.115% √(1-(-.0528) 2 ) and conclude there is no correlation between the two variables.

10. So, maybe the GPAs will show a difference by degree of conservativism (DOC) (instead of by party). those in the 1 - 4 range are designated liberals; those in the 6 - 9 range are designated conservatives (we omit those who answered 5 from this study). Liberals: 47 with average GPA of 3.238 (SD of.3455) Conservatives: 43 with average GPA of 3.092 (SD of.4034) Since GPA and DOC have no correlation, we can consider them independent and use the 2-sample z-test in …

11. H 0 : Same GPA versus H A : liberals have higher GPA Observed difference in GPAs:.146 Se avg for liberals: CF (.3455) /√47 =.04998 Se avg for conserv.: CF (.4034) / √43 =.06105 Se diff = √(. 04998 2 +. 06105 2 ) =.0789 Z = (.146 - 0)/.0789 = 1.85 P-value of 3.2% Reject H 0 and conclude that liberals have higher GPAs.

12. Conclusions What we learned Implications Suspicions