Two candidates A and B stand for an election. Before the election between A and

Question

Two candidates A and B stand for an election. Before the election between A and B, a pre-vote poll was conducted independently on a randomly selected sample of n = 600 individuals. Among the sample, 400 individuals indicate that they will vote for A Assume that the population is in fact neutral to the candidates, i.e., exactly 50% of the population support either A or B. In other words, the population mean proportion of an A vote is assumed to be =0.50 Denote the number of individuals who indicate A in the pre-vote poll asX. You are required to: 1.1) Compute the probability of obtaining this pre-vote poll result under the assumption the population is neutral between the candidates. [40%) 1.2) Discuss whether this pre-vote poll suggests that A will win? An outcome of greater than 50% votes will determine either A or B wins. In your answers, give clear discussions and demonstrate relevant concepts for all of your calculations

Explanation / Answer

Here sample proportion of voters who will vote for A Pr(A) = 400/600 = 2/3

1.1) Here expected number of people who will vote for A as per the true proportion 0.5 is = 600 * 0.5 = 300

standard deviation of number of votes in favour of A = sqrt(0.5 * 0.5 * 600) = 12.247

Here Pr(X >= 400; 300; 12.247) = 1 -BNORM(X < 400; 300; 12.247)

= 1 - Pr(Z < 8.165) = 1 - 1

= 0.000000

1.2)

Yes, as rthe probability is near to 1 so we can assume that A will win. Here an outcome of greater than 50% vots will determine either A or B wins. As the true probability suggests that there is equal chance that both can win. But garnering more than 50% of voters or garnering more than 300 votes have differenet probability than 0.5. There is also an inclusion of tie where both will get same amount of votes.

HEre as pre vote polls suggest high probability of A win it is because there is absolute 1 probability of getting such results in prepoll.

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