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 survey’s 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: Identify the sample proportion and margin of error

The sample proportion \( \hat{p}=0.47 \), and the margin of error \( E = 0.01 \)

Step2: Calculate the lower and upper bounds of the confidence interval

The lower bound of the confidence interval is \( \hat{p}-E\), and the upper bound is \( \hat{p} + E\)

For the lower bound: \(0.47- 0.01=0.46\)

For the upper bound: \(0.47 + 0.01=0.48\)

Answer:

\((0.460,0.480)\)