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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 US Senate to many subjects (dropping subjects who recognize 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 candidate with the better face.  Is there evidence that the proportion of time the candidate with the better face wins is more than 50%?  a)  Explain in words what the parameter p is in this setting.  b)  What the null and alternative hypotheses Ho and Ha?  c)  What is the numerical value of the sample proportion ^p?  The P-value is the probability of what event?  d)  The P-value is P=0.017.  Explain carefully why this is reasonably good evidence that Ho is not true and that Ha is true?

 

Is the result above statistically significant at the 5% level?  At the 1% level?

 

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