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

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

Background Information Personal anecdotal evidence Other studies done?

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)

Basic Political Statistics Number of Democrats: 42 Number of Republicans: 33 Democrats: 1300 Average SAT with SD of Republicans: Average SAT with SD of Democrats: Average GPA with SD of.3652 Republicans: Average GPA with SD of.3666

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%.

H 0 : Same SAT versus H A : Rep. have higher SAT Observed difference: 51.8 Se avg for Dem: CF (122.10) / √42= Se avg for Rep: CF (101.96) / √33 = Se diff = √( ) = Z = ( )/ = 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 = √[( sample size)/2799]

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

Are GPA and Degree of Conservatism related? scale; 1 being most liberal Deleting those who did not respond, we have 111 data points. Using excel’s CORREL function, r = 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 % √(1-(-.0528) 2 ) and conclude there is no correlation between the two variables.

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

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

Conclusions What we learned Implications Suspicions