Question

1 point

In a recent survey, 834 American adults were asked if they would give the U.S. president a favorable job performance rating. Of those surveyed 55% gave the president a favorable rating.

Calculate a confidence interval for the true percent of all American adults who would give a favorable rating for the president.

		(50.43%,59.57%)
		(51.53%,58.47%)
		(54.9%,55.12%)
		(48.13%,61.87%)
		(48.83%,61.17%)

Answer 1

Confidence interval for Population Proportion is given as below:

Confidence Interval = P ± Z* sqrt(P*(1 – P)/n)

Where, P is the sample proportion, Z is critical value, and n is sample size.

We are given

n = 834

P = x/n = 0.55

Confidence level = 95%

Critical Z value = 1.96

(by using z-table)

Confidence Interval = P ± Z* sqrt(P*(1 – P)/n)

Confidence Interval = 0.55 ± 1.96* sqrt(0.55*(1 - 0.55)/834)

Confidence Interval = 0.55 ± 1.96* 0.0172

Confidence Interval = 0.55 ± 0.0338

Lower limit = 0.55 - 0.0338 = 0.5162

Upper limit = 0.55 + 0.0338 = 0.5838

(51.53%, 58.47%)