Answer:
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...