A poll asked the question, "What do you think is the most important problem facing this country today?" Twenty-five percent of the respondents answered "crime and violence." The margin of sampling error was plus or minus 3 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.

UkusakazaL

UkusakazaL

Answered question

2021-08-03

A poll asked the question, "What do you think is the most important problem facing this country today?" Twenty-five percent of the respondents answered "crime and violence." The margin of sampling error was plus or minus 3 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.
Lower limit %
Upper limit %

Answer & Explanation

Tahmid Knox

Tahmid Knox

Beginner2021-08-08Added 1 answers

Step 1
The percentage of responndents answered crime and violence =25%
95% confidence interval margin of error =3%
Theformulato calculate the confidence interval is shown below
Confidence Interval=Sample Statistic±Margin of Error
Step 2
We know sample statistic is given to us as 25%. So substituting the values we get the lower limit and upper limit of 95% confidence interval as shown below.
Lower Limit =22%
Upper Limit =28%
Confidence Interval=Sample Statistic±Margin of Error
Lower Limit=Sample StatisticMargin of Error
Lower Limit=253=22%
Upper Limit=Sample Static+Margin of error
Upper Limit=25+3=28%

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