We often judge other people by their faces. it appears that some people judge candidates for elected office by their faces. researchers showed head‑and‑shoulders photos of the two main candidates in 3232 races for the u. s. senate to many subjects (dropping subjects who recognized one of the candidates) to see which candidate was rated “more competent” based on nothing but the photos. on election day, the candidates whose faces looked more competent won of the 3232 contests. if faces don’t influence voting, half of all races in the long run should be won by the candidate with the better face. is there evidence that the candidate with the better face wins more than half the time?

Yes, the evidence supports the claim that the candidate with the better face wins more than half of the time.

Step-by-step explanation:

We will conduct a hypothesis test for a proportion.  The hypothesis are as follows...

H0:  p = .50

Ha:  p ≠ 0.50

This comes from the statement: "If faces don’t influence voting, half of all races in the long run should be won by the candidate with the better face".  If the actual proportion is significantly higher or lower, then the null will be rejected, so it's a 2 tailed test.

The problem doesn't tell us a confidence level, so we can use 95% (a common value).  See the attached photo for the hypothesis test and conclusion...

the expected value of the random variable : 0, 1 and 2

step-by-step explanation: