Question

A national survey of 1000 adult citizens of a nation found that 25​% dreaded​ Valentine's Day. The margin of error for the survey was 3.6 percentage points with 90​% confidence. Explain what this means.

Answer 1

There is 90% confidence that the proportion of the adult citizens of the nation that dreaded Valentine’s Day is between 0.214 and 0.286.

Explanation:

The summary of the statistics from the information given is ;

At 90% confidence interval, 25​% dreaded​ Valentine's Day and the margin of error for the survey was 3.6 percentage points

SO;

`C.I = \hat p \pm M.O.E`

`C.I = 0.25 \pm 0.036`

C.I = (0.25-0.036 , 0.25+0.036)

C.I = (0.214, 0.286)

The 90% confidence interval for the proportion of the adult citizens of the nation that dreaded Valentine’s day is 0.214 and 0.286.

There is 90% confidence that the proportion of the adult citizens of the nation that dreaded Valentine’s Day is between 0.214 and 0.286.