Step by step
The question
Question: The mean in a sample is 12.6 with a margin of error of 1.2.
Is 14 a plausible value for the mean?
1 What the margin means
12.6 comes from a sample: only some of the people.
The true value for everyone can be a bit different.
The margin of error, 1.2, says how far it can be.
± means plus or minus: we go 1.2 down and 1.2 up.
The true value is likely in between.
2 Lowest and highest
The lowest likely value: 12.6 minus 1.2 is 11.4.
The highest: 12.6 plus 1.2 is 13.8.
3 Draw it
A number line from 10.8 to 14.6: a bit of room on each side.
The likely values go from 11.4 to 13.8.
We colour them green.
12.6, the sample's answer, is right in the middle.
Now 14, the value in the question.
We mark it in red.
4 Inside or outside
14 is above 13.8: outside the green part.
Careful!
Close is not enough.
It must be inside the margin of error.
So no: 14 is not a plausible value.
5 Check
Let's check another way: how far is 14 from 12.6?
14 minus 12.6 is 1.4.
That is more than the margin, 1.2.
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.