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For example I have this problem,

Do Americans tend to vote for the taller of the two candidates in a presidential election? In 30 presidential elections since 1856, 18 of the winners were taller than their opponents. Assume that Americans are not biased by a candidate’s height and that the winner is just as likely to be taller or shorter than his opponent. Find the approximate probability of finding 18 or more of the 30 pairs in which the taller candidate wins.

Based on your answer, can you conclude that Americans consider a candidate’s height when casting their ballot.

To solve this problem I have used normal approximation for binomial distribution. With p=0.5 (because we are assuming that they are unbiased), and found 0.1814

However, I am not sure how to answer the second part of the question, I would like to know at what probability will they consider a candidate's height.

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  • $\begingroup$ The threshold to use is completely up to you. Chances are, though, that the person who set this question doesn't believe that and they think you are going to use a "conventional" value of 0.05. (This is only a cynical guess, though.) BTW, your answer to the first part does not have a direct bearing on the second part, because "vote for the taller" and "consider the candidate's height" are different questions that need to be tested in two different manners! $\endgroup$
    – whuber ♦
    Commented Feb 14, 2019 at 21:52
  • $\begingroup$ i don't think this can be answered with observational data. Anyway what you could do is perform a two-sample t-test, the first group being the winners, the second group being the losers (that competed with the winners at the last stage), and determine whether there is a significant difference in height between the two groups. $\endgroup$
    – user2974951
    Commented Feb 15, 2019 at 8:59

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