Question

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.)

a. Candidate A: 54% Candidate B: 46% Margin of error: ± 5% Confident A would win or Not confident in the outcome
b. Candidate A: 52% Candidate B: 48% Margin of error: ± 1% Confident A would win or Not confident in the outcome
c. Candidate A: 53% Candidate B: 47% Margin of error: ± 2% Confident A would win or Not confident in the outcome
d. Candidate A: 58% Candidate B: 42% Margin of error: ± 10% Confident A would win or Not confident in the outcome

Answer 1

a) Not confident in the outcome.

b) Confident A would win.

c)Confident A would win.

d) Not confident in the outcome.

Explanation:

A confidence interval has two bounds, a lower bound and an upper bound.

These bounds are related to the previous estimate and to the margin of error.

The lower bound is the estimate subtracted by the margin of error.

The upper bound is the margin of error added to the estimate.

Indicate whether we can be relatively confident that candidate A would win if the election were held at the time of the poll.

Here, we need the lower bound of the confidence interval for the percentage of votes of the candidate A above 50%.

a. Candidate A: 54% Candidate B: 46% Margin of error: ± 5% Confident A would win or Not confident in the outcome

54 - 5 = 49%

Not confident in the outcome.

b. Candidate A: 52% Candidate B: 48% Margin of error: ± 1% Confident A would win or Not confident in the outcome

52 - 1 = 51%

Confident A would win.

c. Candidate A: 53% Candidate B: 47% Margin of error: ± 2% Confident A would win or Not confident in the outcome

53 - 2 = 51%

Confident A would win.

d. Candidate A: 58% Candidate B: 42% Margin of error: ± 10% Confident A would win or Not confident in the outcome

58 - 10 = 48%

Not confident in the outcome.