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Chapter 13: Confidence Intervals: Making Your Best Guesstimate

As the confidence level increases, the number of standard errors increases, so
the margin of error increases.
Table 13-1
Confidence Level
z*-value
80% z*-values for Various Confidence Levels 199
1.28
90% 1.645 (by convention)
95% 1.96
98% 2.33
99% 2.58
If you want to be more than 95% confident about your results, you need to
add and subtract more than about two standard errors. For example, to be
99% confident, you would add and subtract about two and a half standard
errors to obtain your margin of error (2.58 to be exact). The higher the con-
fidence level, the larger the z*-value, the larger the margin of error, and the
wider the confidence interval (assuming everything else stays the same). You
have to pay a certain price for more confidence.

Note that I said “assuming everything else stays the same.” You can offset an
increase in the margin of error by increasing the sample size. See the follow-
ing section for more on this.

Factoring In the Sample Size

The relationship between margin of error and sample size is simple: As the
sample size increases, the margin of error decreases, and the confidence
interval gets narrower. This relationship confirms what you hope is true: The
more information (data) you have, the more accurate your results are going
to be. (That, of course, assumes that the information is good, credible infor-
mation. See Chapter 3 for how statistics can go wrong.)
The margin of error formulas for the confidence intervals in this chapter all
involve the sample size (n) in the denominator. For example, the formula for
margin of error for the sample mean, (which you’ll see in great detail
later in this chapter), has an n in the denominator of a fraction (this is the
case for most margin of error formulas). As n increases, the denominator of this
fraction increases, which makes the overall fraction get smaller. That makes the
margin of error smaller and results in a narrower confidence interval.

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