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 (0.460, 480)
(round to three decimal places as needed.)
use the results from the newer survey.
the interval is a 75.4% confidence interval.
(round to one decimal place as needed.)
use the results from three weeks prior to the newer survey.
the confidence interval for the proportion is (□□)
(round to three decimal places as needed.)

Explanation:

Step1: Calculate the confidence interval for the proportion three weeks prior

The formula for a confidence interval for a proportion is $\hat{p}\pm E$, where $\hat{p}$ is the sample proportion and $E$ is the margin of error.
Given $\hat{p} = 0.53$ and $E=0.01$.
Lower bound: $0.53 - 0.01=0.52$
Upper bound: $0.53 + 0.01 = 0.54$

Answer:

The confidence interval for the proportion is $(0.520, 0.540)$