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 200 voters finds that 98 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 0.52? 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 0.52? The probability that less than 98 people voted for the referendum is Q. (Round to four decimal places as needed.)

Explanation / Answer

We first get the z score for the critical value:          
          
x = critical value =    97.5      
u = mean = np =    104      
          
s = standard deviation = sqrt(np(1-p)) =    7.065408693      
          
Thus, the corresponding z score is          
          
z = (x-u)/s =    -0.91997509      
          
Thus, the left tailed area is          
          
P(z <   -0.91997509   ) =    0.178792888 [ANSWER]

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Hi! If you don't use continuity correction, then this is the alternate solution:

We first get the z score for the critical value:          
          
x = critical value =    98      
u = mean = np =    104      
          
s = standard deviation = sqrt(np(1-p)) =    7.065408693      
          
Thus, the corresponding z score is          
          
z = (x-u)/s =    -0.849207776      
          
Thus, the left tailed area is          
          
P(z <   -0.849207776   ) =    0.197882844 [ALTERNATE ANSWER]

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