Question

A national survey of 1000 adult citizens of a nation found that 15​% dreaded​ Valentine's Day. The margin of error for the survey was 6.2 percentage points with 85​% confidence. Explain what this means.

Answer 1

We are 85% confident that the proportion of adults who dreaded valentines day is within the range of 8.8% to 21.2%.

Step-by-step explanation:

Proportion of adults who dreaded valentines day = 15% = 0.15

The margin of error with 85% confidence = 6.2% = 0.062

The confidence interval is given by

p ± margin of error

0.15 ± 0.062

Lower limit = 0.15 - 0.062

Lower limit = 0.088

Lower limit = 8.8%

Upper limit = 0.15 + 0.062

Upper limit = 0.212

Upper limit = 21.2%

So it means that we are 85% confident that the proportion of adults who dreaded valentines day is within the range of 8.8% to 21.2%.