Question

A poll conducted the day before the student-body presidential election at a Midwestern university showed that 53 percent favored Mario, the rest favoring Yin Ling. The margin of error was 5 percentage points. A) Find the confidence interval of Mario. B) Should Yin Ling have conceded the election? (HINT : Mean +/- Margin of Error)

Answer 1

(A) The confidence interval for the proportion of students who favored Mario is (48%, 58%).

(B) Yin Ling should not concede the election.

Explanation:

The (1 - α)% confidence interval for the population proportion is:

`CI=\hat p\pm MOE`

The proportion of students who favored Mario is,
`\hat p = 0.53`.

The margin of error is, MOE = 0.05.

(A)

Compute the confidence interval for the proportion of students who favored Mario as follows:

`CI=\hat p\pm MOE\\=0.53\pm 0.05\\=(0.48, 0.58)`

Thus, the confidence interval for the proportion of students who favored Mario is (48%, 58%).

(B)

The confidence interval for Mario shows that 48% to 58% people are expected to favor Mario.

Since the lower limit is 48% there is still a chance that Yin Ling could win the election if only 48% students favor Mario.

So, Yin Ling should not concede the election.