Question

translate the statement into a confidence interval. approximate the level of confidence.
in a survey of 3373 adults in a country, 47% believe the economy is getting better. three weeks prior to this survey, 53% believed that the economy was getting better. the surveys margin of error is ±1%.
use the results from the newer survey.
the confidence interval for the proportion is (
(round to three decimal places as needed.)

Explanation:

Step1: Calculate the lower bound

The sample proportion \(p = 0.47\) and the margin of error \(E=0.01\). The lower bound of the confidence interval is \(p - E\).
\(0.47- 0.01=0.46\)

Step2: Calculate the upper bound

The upper bound of the confidence interval is \(p + E\).
\(0.47 + 0.01=0.48\)

Answer:

\((0.46,0.48)\)