Question

A poll asked the question, "What do you think is the most important problem facing this country today?" Twenty-three percent of the respondents answered "crime and violence." The margin of sampling error was plus or minus 4 percentage points. Following the convention that the margin of error is based on a 95% confidence interval, find a 95% confidence interval for the percentage of the population that would respond "crime and violence" to the question asked by the pollsters.

Answer 1

We are given with
X = 23%
s = 4%
CI = 95 % (z = 1.96)
let n as the number of samples

The intervals are
x + z (s/√n)
and
x - z (s/√n)

substitute the given values and if n is given, you can get the exact values