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 300 voters finds that 156 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 0.49​? 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 0.49​? The probability that more than 156 people voted for the referendum is nothing. ​(Round to four decimal places as​ needed.) Comment on the dangers of using exit polling to call elections. Choose the correct answer below. A. The result is unusual because the probability that ModifyingAbove p with caret is equal to or more extreme than the sample proportion is greater than​ 5%. Thus, it is not unusual for a wrong call to be made in an election if exit polling alone is considered. B. The result is not unusual because the probability that ModifyingAbove p with caret is equal to or more extreme than the sample proportion is greater than​ 5%. Thus, it is not unusual for a wrong call to be made in an election if exit polling alone is considered. C. The result is unusual because the probability that ModifyingAbove p with caret is equal to or more extreme than the sample proportion is less than​ 5%. Thus, it is unusual for a wrong call to be made in an election if exit polling alone is considered. D. The result is not unusual because the probability that ModifyingAbove p with caret is equal to or more extreme than the sample proportion is less than​ 5%. Thus, it is unusual for a wrong call to be made in an election if exit polling alone is considered.

Answer 1

n = 300

p = 0.49

= 0.49

= sqrt(p(1 - p)/n)

       = sqrt(0.49(1 - 0.49)/300)

       = 0.0289

= 156/300 = 0.52

P( > 0.52)

= P(( - )/ > (0.52 - )/)

= P(Z > (0.52 - 0.49)/0.0289)

= P(Z > 1.038)

= 1 - P(Z < 1.038)

= 1 - 0.8504

= 0.1496

Option - B) The result is not unusual because the probability that is equal to or more extreme than the sample proportion is greater than 5%. Thus, it is not unusual for a wrong call to be made in an election if exit polling alone is considered.