We often judge other people by their faces. It appears that some people judge candidates for...

We often judge other people by their faces. It appears that some people judge candidates for elected office by their faces. Psychologists showed headand-shoulders photos of the two main candidates in 32 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 22 of the 32 contests.

a) Plot the log-likelihood function for these data in R.

b) Based on your plot, what is the approximate maximum likelihood estimate of the probability that the candidate who appears more competent will win the election?

c) Estimate the 95% confidence interval for your answer to part b.

d) Use the likelihood ratio test or the binomial test to test the null hypothesis that the probability is 0.5. Can you reject this null hypothesis?

Expert Solution

We often judge other people by their faces. It appears that some people judge candidates for elected office by their faces. Psychologists showed head and-shoulders photos of the two main candidates in 32 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 22 of the 32 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 proportion of times the candidate with the better face wins is more than 50%?

(a) Explain in words what the parameter p is in this setting.

proportion of times the candidate with the better face wins

(b) What are the null and alternative hypotheses H0 and Ha?

upper tail test

(c) What is the numerical value of the sample proportion ˆp? The P-value is the probability of what event?

p=22/32=0.6875

(d) Calculate the P-value. Explain carefully why this is reasonably good evidence that H0 is not true and that Ha is true.

=2.1213

milcah answered 5 hours ago

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