13. Exit polling is a popular technique used to determine the outcome of an elec
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Question
13. 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 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 __?__. (Round to four decimal places as needed.)
Comment on the dangers of using exit polling to call elections. Choose the correct answer below.
MULTIPLE CHOICE
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 is considered.
b. The result is not unusual because the probability that ^p 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 not unusual because the probability that ^p 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 unusual because the probability that ^p 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.
Explanation / Answer
Solution:- The probability that fewer than 245 people voted for the referendum is 0.1738.
p = 0.51
n = 500
x = 245
By applying binomial distributiion:-
P(x,n) = nCx*px*(1-p)(n-x)
P(x < 245) = 0.1738
The probability that fewer than 245 people voted for the referendum is 0.1738.
b. The result is not unusual because the probability that ^p 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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