A survey of students says 70% with a margin of error of 6%. Is 80% a… Step by Step

Step by step

The question

Question: A survey of students says 70% with a margin of error of 6%.

Is 80% a plausible value?

1 What the margin means

70% comes from a sample: only some of the people.

The true value for everyone can be a bit different.

The margin of error, 6%, says how far it can be.

70% ± 6%

± means plus or minus: we go 6% down and 6% up.

The true value is likely in between.

± = plus or minus

true value: likely within 6% of 70%

2 Lowest and highest

The lowest likely value: 70% minus 6% is 64%.

lowest = 70% − 6% = 64%

The highest: 70% plus 6% is 76%.

highest = 70% + 6% = 76%

3 Draw it

A number line from 60 to 84: a bit of room on each side.

The likely values go from 64% to 76%.

We colour them green.

70%, the sample's answer, is right in the middle.

Now 80%, the value in the question.

We mark it in red.

4 Inside or outside

80% is above 76%: outside the green part.

= 80% > 76%

Careful!

Close is not enough.

It must be inside the margin of error.

Careful: not 80% is close to 70% → plausible ✗

So no: 80% is not a plausible value.

= no, 80% is not plausible

5 Check

Let's check another way: how far is 80% from 70%?

80% minus 70% is 10%.

That is more than the margin, 6%.

So it is right!

80% − 70% = 10%, 10% > 6%

Let's look back.

First: what the margin means.

Then: lowest and highest.

Then: draw it.

Then: inside or outside.

Last: check.

Answer