A survey says 30% with a margin of error of 3.5%. Is 27% a plausible… Step by Step

Step by step

The question

Question: A survey says 30% with a margin of error of 3.5%.

Is 27% a plausible value?

1 What the margin means

30% comes from a sample: only some of the people.

The true value for everyone can be a bit different.

The margin of error, 3.5%, says how far it can be.

30% ± 3.5%

± means plus or minus: we go 3.5% down and 3.5% up.

The true value is likely in between.

± = plus or minus

true value: likely within 3.5% of 30%

2 Lowest and highest

The lowest likely value: 30% minus 3.5% is 26.5%.

lowest = 30% − 3.5% = 26.5%

The highest: 30% plus 3.5% is 33.5%.

highest = 30% + 3.5% = 33.5%

3 Draw it

A number line from 24.6 to 35.4: a bit of room on each side.

The likely values go from 26.5% to 33.5%.

We colour them green.

30%, the sample's answer, is right in the middle.

Now 27%, the value in the question.

We mark it in red.

4 Inside or outside

27% is between 26.5% and 33.5%: inside the green part.

= 26.5% ≤ 27% ≤ 33.5%

Careful!

Plausible means likely.

It does not mean the true value is 27% for sure.

Careful: plausible = likely, not sure

So yes: 27% is a plausible value.

= yes, 27% is plausible

5 Check

Let's check another way: how far is 27% from 30%?

30% minus 27% is 3%.

That is within the margin, 3.5%.

So it is right!

30% − 27% = 3%, 3% ≤ 3.5%

Let's look back.

First: what the margin means.

Then: lowest and highest.

Then: draw it.

Then: inside or outside.

Last: check.

Answer