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 400400 voters finds that 208208 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 0.490.49? 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 0.490.49?

What we want to do is find the probability of the sample occurring based on the results of the poll being 0.49. Since we have decimals, we are working with proportions. We have

n = 400

p-hat = 208/400 = 0.52

p = 0.49

We first need to calculate the z-score for this situation. See attached photo 1 for the calculation.

The z-score was 0.12, which has a probability of 0.5478

That means there is about a 54.78% chance that the sample poll is a result of random chance.

The problem with exit polls are that they can come from a biased sample. The place they took the poll at could be mostly one sided in their voting preference (democrat or republican). Also, a sample size of only 400 in a town that has a population of over 100,000 isn't a very good representation of the population.