Answer:
A) The probability is 0.0838.
B) the use of exit polling to call elections is dangerous event.
Explanation:
We are given;
A referendum to increase funding for education is on the ballot in a large town (voting population over 100,000)
Number voters in an exit poll; N = 300
Number of voters who favored referendum; X = 144
probability of sample proportion if the population proportion of voters in the town in favor of the referendum; p = 0.51
Sample proportion of voters who favored referendum is given as,
p' = 144/300
p' = 0.47
Using the central limit theorem, the sampling distribution of proportion for a large sample size of 300,follows normal distribution with mean same as population proportion and standard deviation given by the formula;
s = √(p(1 - p)/n
s = √(0.51(1 - 0.51)/300
s = 0.028862
np = 300 x 0.51 = 153
n(1 - p) = 300(1 - 0.51)
n(1 - p) = 147
np and n(1 - p) are both greater than 5,thus;
the probability of sample proportion if the population proportion of voters in the town in favor of the referendum is 0.51 is expressed as follows,
P(p > p') = P(Z < (p'- p)/s)
P(p > p') = P(Z < (0.47 - 0.51)/0.028862)
P(p > p') = P(Z < - 1.386)
From the table i attached, the z value is 0.0838
Thus, the probability of occurrence of sample proportion given the population proportion of voters in the town in favor of the referendum of 0.51 is 0.0838
Based on these results, it is observed that the exit poll proportion result is a rare event with very less probability of occurrence. Hence, if translated for entire population, it might lead to incorrect results.
Hence the use of exit polling to call elections is dangerous event.