Throughout the US presidential election of 2012, polls gave regular updates on the sample proportion supporting each candidate and the margin of error for the estimates. This attempt to predict the outcome of an election is a common use of polls. In each case below, the proportion of voters who intend to vote for each candidate is given as well as a margin of error for the estimates. Indicate whether we can be relatively confident that candidate A would win if the election were held at the time of the poll. (Assume the candidate who gets more than of the vote wins.)

Question

04-04-2020
Mathematics

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Throughout the US presidential election of 2012, polls gave regular updates on the sample proportion supporting each candidate and the margin of error for the estimates. This attempt to predict the outcome of an election is a common use of polls. In each case below, the proportion of voters who intend to vote for each candidate is given as well as a margin of error for the estimates. Indicate whether we can be relatively confident that candidate A would win if the election were held at the time of the poll. (Assume the candidate who gets more than of the vote wins.)

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AyBaba7 AyBaba7 · Answer 1 · 2020-04-04T05:31:51+02:00

Answer:

1.) We cannot say for certain which candidate will win. But A has a statistical edge.

2.) We can say certainly that candidate A will win the election; albeit with a not so big margin.

3.) Candidate A will win this election based on the results of the final poll's before the election.

4.) We cannot say for certain which candidate will win. But A has a statistical edge.

The reasons are explained below.

Step-by-step explanation:

Confidence interval expresses a range of values in the distribution where the true proportion or mean can be found with some level of confidence.

Confidence Interval = (Sample Mean or Proportion) ± (Margin of error)

1. Candidate A: 54% & Candidate B:46% with Margin of error: + 5%

The confidence interval for candidate A

(54%) ± (5%) = (49%, 59%)

The confidence interval for candidate B

(46%) ± (5%) = (41%, 51%)

Since values greater than 50% occur in both intervals, we cannot say for certain that either of the two candidates will outrightly win the election. It just slightly favours candidate A who has A bigger range of confidence interval over 50% for the true sample proportion to exist in.

2. Candidate A: 52% & Candidate B:48% with Margin of error: + 1%

The confidence interval for candidate A

(52%) ± (1%) = (51%, 53%)

The confidence interval for candidate B

(48%) ± (1%) = (47%, 49%)

Here, it is outrightly evident that candidate A will win the elections based on the result of the final polls. The overall range of the confidence interval that contains the true sample proportion of voters that support candidate A is totally contained in a region that is above 50%. So, candidate A wins this one, easily; albeit with a close margin though.

3. Candidate A: 53% & Candidate B:47% with Margin of error: + 2%

The confidence interval for candidate A

(53%) ± (2%) = (51%, 55%)

The confidence interval for candidate B

(47%) ± (2%) = (45%, 49%)

Here too, it is outrightly evident that candidate A will win the elections based on the result of the final polls. The overall range of the confidence interval that contains the true sample proportion of voters that support candidate A is totally contained in a region that is above 50%. Hence, statistics predicts that candidate A wins this one.

4. Candidate A: 58% & Candidate B:42% with Margin of error: + 10%

The confidence interval for candidate A

(58%) ± (10%) = (48%, 68%)

The confidence interval for candidate B

(42%) ± (10%) = (32%, 52%)

Since values greater than 50% occur in both intervals, we cannot say for certain that either of the two candidates will outrightly win the election. It just slightly favours candidate A who has A bigger range of confidence interval over 50% for the true sample proportion to exist in.

Hope this Helps!!!