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Part IV: Guesstimating and Hypothesizing with Confidence
The number of standard errors you have to add or subtract to get the MOE

depends on how confident you want to be in your results (this is called your
confidence level). Typically, you want to be about 95% confident, so the basic
rule is to add or subtract about 2 standard errors (1.96, to be exact) to get the
MOE (you get this from the Empirical Rule; see Chapter 9). This allows you to
account for about 95% of all possible results that may have occurred with
repeated sampling. To be 99% confident, you add and subtract 2.58 standard
errors. (This assumes a normal distribution on large n; standard deviation
known. See Chapter 11.)
You can be more precise about the number of standard errors you have to add
or subtract in order to calculate the MOE for any confidence level; if the condi-
tions are right, you can use values on the standard normal (Z-) distribution. (See
Chapter 13 for details.) For any given confidence level, a corresponding value
on the standard normal distribution (called a z*-value) represents the number
of standard errors to add and subtract to account for that confidence level.
For 95% confidence, a more precise z*-value is 1.96 (which is “about” 2), and
for 99% confidence, the exact z*-value is 2.58. Some of the more commonly
used confidence levels (also known as percentage confidence), along with
their corresponding z*-values, are given in Table 12-1.
Table 12-1 z*-Values for Selected (Percentage)
Confidence Levels
Percentage Confidence z*-Value
80 1.28
90 1.645
95 1.96
98 2.33
99 2.58
To find a z*-value like those in Table 12-1, add to the confidence level to make
it a less-than probability and find its corresponding z-value on the Z-table. For
example, a 95% confidence level means the “between” probability is 95%, so
the “less-than” probability is 95% plus 2.5% (half of what’s left), or 97.5%. Look
up 0.975 in the body of the Z-table and find z * = 1.96 for a 95% confidence level.
Calculating margin of error
for a sample proportion

When a polling question asks people to choose from a range of answers
(for example, “Do you approve or disapprove the president’s performance?”),

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