Exit polling is a popular technique used to determine the outcome of an election

Question

Exit polling is a popular technique used to determine the outcome of an election prior to results being tallied. Suppose a referendum to increase funding for education is on the ballot in a large town (voting population over 100,000). An exit poll of 500 voters finds that 240 voted for the referendum. How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0.51? Based on your result, comment on the dangers of using exit polling to call elections.

How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0.51?

The probability that fewer than 240 people voted for the referendum is ? (round to four decimal places)

Explanation / Answer

phat=240/500 = 0.48
The probability is
P(phat < 0.48) = P((phat-p)/sqrt(p*(1-p)/n) < (0.48-0.51)/sqrt(0.51*(1-0.51)/500))
=P(Z< -1.3419) = 0.0898 (from standard normal table)
Since the probability is larger than 0.05, we can conclude that it is likely

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