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
200 voters finds that 92 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 92 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 Modifying Above p with care tp 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 is not unusual because the probability that Modifying Above p with care tp 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.
C.
The result is not is not unusual because the probability that
Modifying Above p with care tp is equal to or more extreme than the sample proportion is greater than 5%. Thus, it is not is not
unusual for a wrong call to be made in an election if exit polling alone is considered.
D.
The result is unusual because the probability that Modifying Above p with care tp 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.
Solution:
The probability that fewer than 92 people voted for the referendum is:
Now using the z-score formula, we have:
Now using the standard normal table, we have:
Therefore, the probability that fewer than 92 people voted for the referendum is 0.0786
Comment on the dangers of using exit polling to call elections. Choose the correct answer below.
Answer: C. 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.
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