A poll asked the question What do you think is the most impo

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 2 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.

Solution

lower limit : 0.23-0.02 = 0.21 (i.e. 21%)

upper limit: 0.23+0.02 =0.25 (i.e. 25%)