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 245 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 0.52? 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 0.52?

Answer 1

To determine the likelihood of the sample results, we can use statistical inference. In this case, we can perform a hypothesis test using the binomial distribution.

Given that the sample size is 500 and the sample proportion in favor of the referendum is 245/500 = 0.49, we can calculate the probability of obtaining 245 or more "yes" votes out of 500 under the assumption that the population proportion is 0.52.

Using statistical software or a binomial probability calculator, we can find this probability. In this case, assuming a population proportion of 0.52, the probability of obtaining 245 or more "yes" votes out of 500 is relatively low.

This means that the sample result of 245 "yes" votes out of 500 is unlikely if the true population proportion is indeed 0.52. It suggests that the sample result may not accurately reflect the population's opinion.

Therefore, using this sample result from the exit poll to predict the outcome of the election can be problematic and potentially misleading. Exit polling has inherent limitations, including sampling bias, nonresponse bias, and variability, which can lead to inaccurate predictions of election outcomes. It is crucial to interpret exit poll results with caution and consider other factors and methods for a more accurate assessment of election results.