Question

translate the statement into a confidence interval. approximate the level of confidence.
in a survey of 1019 adults in a country, 73% said being able to speak the language is at the core of national identity. the surveys margin of error is ±3.8%.
the confidence interval for the proportion is
(round to three decimal places as needed.)

Explanation:

Step1: Calculate the confidence interval

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 \(\hat{p} = 0.73\) and \(E=0.038\).
The lower bound is \(\hat{p}-E=0.73 - 0.038=0.692\).
The upper bound is \(\hat{p}+E=0.73+ 0.038 = 0.768\).

Answer:

The confidence interval for the proportion is \((0.692,0.768)\)