Exit polling is used to determine the outcome of an election

Exit polling is used to determine the outcome of an election prior to tallying results. Suppose a referendum to increase funding for a purpose education is on the ballot in a large town (voting population over 100,000). An exit poll of 500 voters finds that 255 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 0.48?_____ (round answer four decimal places.)

Solution

phat=255/500 = 0.51

The probability is

P(phat>0.51) = P((phat-p)/sqrt(p*(1-p)/n) >(0.51-0.48)/sqrt(0.48*(1-0.48)/500))

=P(Z>1.34) = 0.0901 (from standard normal table)

Since the probability is larger than 0.05, we can conclude that it is likely