Step by step
The question
Question: The mean time in a sample is 24 minutes with a margin of error of 2.5 minutes.
Is 21 minutes a plausible value for the mean?
1 What the margin means
24 minutes comes from a sample: only some of the people.
The true value for everyone can be a bit different.
The margin of error, 2.5 minutes, says how far it can be.
± means plus or minus: we go 2.5 minutes down and 2.5 minutes up.
The true value is likely in between.
2 Lowest and highest
The lowest likely value: 24 minus 2.5 is 21.5.
The highest: 24 plus 2.5 is 26.5.
3 Draw it
A number line from 19.6 to 27.8: a bit of room on each side.
The likely values go from 21.5 to 26.5.
We colour them green.
24, the sample's answer, is right in the middle.
Now 21, the value in the question.
We mark it in red.
4 Inside or outside
21 is below 21.5: outside the green part.
Careful!
Close is not enough.
It must be inside the margin of error.
So no: 21 minutes is not a plausible value.
5 Check
Let's check another way: how far is 21 from 24?
24 minus 21 is 3.
That is more than the margin, 2.5.
So it is right!
Let's look back.
First: what the margin means.
Then: lowest and highest.
Then: draw it.
Then: inside or outside.
Last: check.