Exit polling is a popular technique used to determine the outcome of an election

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 400 voters finds that 204 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 204 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. 0 A. 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 0 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 wrong call to be made in an election if exit polling alone is considered 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 0 D. 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

Explanation / Answer

Given that,
possibile chances (x)=204
sample size(n)=400
success rate ( p )= x/n = 0.51
success probability,( po )=0.49
failure probability,( qo) = 0.51
null, Ho:p=0.49  
alternate, H1: p>0.49
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.64
since our test is right-tailed
reject Ho, if zo > 1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.51-0.49/(sqrt(0.2499)/400)
zo =0.8002
| zo | =0.8002
critical value
the value of |z | at los 0.05% is 1.64
we got |zo| =0.8 & | z | =1.64
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: right tail - Ha : ( p > 0.80016 ) = 0.21181
hence value of p0.05 < 0.21181,here we do not reject Ho
ANSWERS
---------------
null, Ho:p=0.49
alternate, H1: p>0.49
test statistic: 0.8002
critical value: 1.64
decision: do not reject Ho
p-value: 0.2118

this result is not unusual because the probability that p is equal to the sample proportion is less than 5%. thus , it is not unusual for a wrong call to be in an election if exit polling is alone consider

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