Step by step
The question
Question: The mean sleep in a sample is 6.2 hours with a margin of error of 0.4 hours.
Is 7 hours a plausible value for the mean?
1 What the margin means
6.2 hours comes from a sample: only some of the people.
The true value for everyone can be a bit different.
The margin of error, 0.4 hours, says how far it can be.
± means plus or minus: we go 0.4 hours down and 0.4 hours up.
The true value is likely in between.
2 Lowest and highest
The lowest likely value: 6.2 minus 0.4 is 5.8.
The highest: 6.2 plus 0.4 is 6.6.
3 Draw it
A number line from 5.5 to 7.2: a bit of room on each side.
The likely values go from 5.8 to 6.6.
We colour them green.
6.2, the sample's answer, is right in the middle.
Now 7, the value in the question.
We mark it in red.
4 Inside or outside
7 is above 6.6: outside the green part.
Careful!
Close is not enough.
It must be inside the margin of error.
So no: 7 hours is not a plausible value.
5 Check
Let's check another way: how far is 7 from 6.2?
7 minus 6.2 is 0.8.
That is more than the margin, 0.4.
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.