Question

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 0.51? 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 245 people voted for the referendum is 0.1855. (Round to four decimal places as needed.) Comment on the dangers of using exit polling to call elections. Choose the correct answer below. O A. The result is unusual because the probability that p 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 considered. O B. The result is not unusual because the probability that p 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. O C. The result is 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. O D. The result is not unusual because the probability that is equal to or more extreme than the sample proportion is greater than 5%. Thus, is not unusual for a wrong call to be made in an election if exit polling alone is considered.

Answer 1

The probability of the sample result being equal to or more extreme than the hypothesized population proportion of 0.51 is 0.1855 (18.55%). This value is greater than the 5% threshold, indicating the sample result is not unusual. Consequently, reliance on exit polling alone could lead to incorrect predictions in election outcomes, demonstrating Option D as the correct choice.

Step-by-step explanation:

When assessing the likelihood of the results of an exit poll, statisticians determine if the sample proportion falls within a certain range around the population proportion. If the population proportion of voters in the town in favor of the referendum is 0.51, and a sample of 500 voters finds that 245 voted for the referendum, we would expect the sample proportion (p') to be close to 0.51.

In this case, 245 out of 500 is a sample proportion of 0.49, which is close to the hypothesized population proportion of 0.51. Considering the given probability that fewer than 245 people would vote for the referendum is 0.1855, and applying the concept of errors in exit polls, we can say that:

• If the probability that the sample proportion is equal to or more extreme than the hypothesized proportion is less than 0.05 (5%), we would consider the result unusual.
• However, in this case, the probability of 0.1855 (18.55%) is greater than 5%, which indicates that the result is not unusual. This means that a wrong call could be made in the election if exit polling alone is considered.

Therefore, the correct answer is Option D: 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.