Question

translate the statement into a confidence interval. approximate the level of confidence.
in a survey of 1048 adults in a country, 71% said being able to speak the language is at the core of national identity. the surveys margin of error is ±3.1%.
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 is \(\hat{p}-E\), where \(\hat{p} = 0.71\) (since \(71\%=0.71\)) and \(E = 0.031\) (since \(3.1\%=0.031\)).
\(0.71 - 0.031=0.679\)

Step2: Calculate the upper bound of the confidence interval

The formula for the upper bound is \(\hat{p}+E\).
\(0.71+ 0.031 = 0.741\)

Answer:

\((0.679,0.741)\)