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Chapter 13: Confidence Intervals: Making Your Best Guesstimate
Suppose you want to know the percentage of vehicles in the U.S. that are
pickup trucks (that’s the parameter, in this case). You can’t look at every
single vehicle, so you take a random sample of 1,000 vehicles over a range
of highways at different times of the day. You find that 7% of the vehicles in
your sample are pickup trucks. Now, you don’t want to say that exactly 7%
of all vehicles on U.S. roads are pickup trucks, because you know this is only
based on the 1,000 vehicles you sampled. Though you hope 7% is close to
the true percentage, you can’t be sure because you based your results on a 195
sample of vehicles, not on all the vehicles in the U.S.
So what to do? You take your sample result and add and subtract some
number to indicate that you are giving a range of possible values for the pop-
ulation parameter, rather than just assuming the sample statistic equals the
population parameter (which would not be good, although it’s done in the
media all the time). This number that is added to and subtracted from a sta-
tistic is called the margin of error (MOE ). This plus or minus (denoted by ±)
that’s added to any estimate helps put the results into perspective. When you
know the margin of error, you have an idea of how much the sample results
could change if you took another sample.
The word error in margin of error doesn’t mean a mistake was made or the
quality of the data was bad. It just means the results from a sample are not
exactly equal to what you would have gotten if you had used the entire popu-
lation. This gap measures error due to random chance, the luck of the draw —
not due to bias. (That’s why minimizing bias is so important when you select
your sample and collect your data; see Chapters 16 and 17.)

Getting with the Jargon

A statistic plus or minus a margin of error is called a confidence interval:

✓ The word interval is used because your result becomes an interval.
For example, say the percentage of kids who like baseball is 40%, plus
or minus 3.5%. That means the percentage of kids who like baseball is
somewhere between 40% – 3.5% = 36.5% and 40% + 3.5% = 43.5%. The
lower end of the interval is your statistic minus the margin of error, and
the upper end is your statistic plus the margin of error.
✓ With all confidence intervals, you have a certain amount of confidence
in being correct (guessing the parameter) with your sample in the long
run. Expressed as a percent, the amount of confidence is called the
confidence level.

You can find formulas and examples for the most commonly used confidence
intervals later in this chapter.

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