Question

translate the statement into a confidence interval. approximate the level of confidence.
in a survey of 1100 adults in a country, 67% think teaching is one of the most important jobs in the country today. the surveys margin of error is ±3%.
the confidence interval for the proportion is (□,□).
(round to three decimal places as needed.)

Explanation:

Step1: Calculate the lower bound of the confidence interval

The formula for the lower bound of a confidence interval for a proportion is \(\hat{p}-E\), where \(\hat{p}\) is the sample proportion and \(E\) is the margin of error.
Given \(\hat{p} = 0.67\) and \(E=0.03\), the lower bound is \(0.67 - 0.03=0.64\)

Step2: Calculate the upper bound of the confidence interval

The formula for the upper bound of a confidence interval for a proportion is \(\hat{p}+E\)
Using \(\hat{p} = 0.67\) and \(E = 0.03\), the upper bound is \(0.67+0.03 = 0.70\)

Answer:

\((0.64,0.70)\)