Question

A political pollster is conducting an analysis of sample results in order to make predictions on election night. Assuming a two-candidate election, if a specific candidate receives at least 54% of the vote in the sample, that candidate will be forecast as the winner of the election. You select a random sample of 100 voters. Complete parts (a) through (c) below. The probability is 0.2177 that a candidate will be forecast as the winner when the population percentage of her vote is 50.1% Round to four decimal places as needed.) b. What is the probability that a candidate will be forecast as the winner when the population percentage of her vote is 60%? The probability is .8897 that a candidate will be forecast as the winner when the population percentage of her vote is 60% (Round to four decimal places as needed.) C. What is the probability that a candidate will be forecast as the winner when the population percentage of her vote is 49% and she will actually lose the election? The probability is that a candidate will be forecast as the winner when the population percentage of her vote is 49% Round to four decimal places as needed.) Enter your answer in the answer box and then click Check Answer parts remaining Clear All Check Answer

Answer 1

The probability that a candidate will be forecast as the winner when their population vote percentage is 60% is given as 0.8897, and this informs our understanding of population proportion and polling confidence in an election context.

Step-by-step explanation:

The question involves the topic of population proportion which is a concept frequently used in statistics, especially concerning election polls. When determining the probability of a candidate being forecast as the winner, it is assumed that this probability changes based on the actual population percentage of the votes the candidate receives. Specifically, these probabilities change significantly for a candidate with 50.1% of the vote compared to one with 60% of the vote. For the case of 60%, we are given that the probability of being forecast as the winner is 0.8897.

For a candidate with 49% of the vote, we are interested in the probability that the candidate would still be forecast as the winner even though they will actually lose the election. This would require a calculation based on the sampling distribution, with the understanding that the probability will be low as the candidate's actual vote percentage is below the 54% threshold needed for the forecast to be a predicted win in the sample.