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Part IV: Guesstimating and Hypothesizing with Confidence
Three factors affect the width of a confidence interval:
✓ Confidence level
✓ Sample size
✓ Amount of variability in the population
Each of these three factors plays an important role in influencing the width
of a confidence interval. In the following sections, you explore details of each
element and how they affect width.
Choosing a Confidence Level
Every confidence interval (and every margin of error, for that matter) has a
percentage associated with it that represents how confident you are that the
results will capture the true population parameter, depending on the luck of the
draw with your random sample. This percentage is called a confidence level.

A confidence level helps you account for the other possible sample results
you could have gotten, when you’re making an estimate of a parameter using
the data from only one sample. If you want to account for 95% of the other
possible results, your confidence level would be 95%.

What level of confidence is typically used by researchers? I’ve seen confidence
levels ranging from 80% to 99%. The most common confidence level is 95%. In
fact, statisticians have a saying that goes, “Why do statisticians like their jobs?
Because they have to be correct only 95% of the time.” (Sort of catchy, isn’t it?
And let’s see weather forecasters beat that.)

Variability in sample results is measured in terms of number of standard
errors. A standard error is similar to the standard deviation of a data set, only
a standard error applies to sample means or sample percentages that you
could have gotten if different samples were taken. (See Chapter 11 for infor-
mation on standard errors.)

Standard errors are the building blocks of confidence intervals. A confidence
interval is a statistic plus or minus a margin of error, and the margin of error is
the number of standard errors you need to get the confidence level you want.
Every confidence level has a corresponding number of standard errors that
have to be added or subtracted. This number of standard errors is a called a
critical value. In a situation where you use a Z-distribution to find the number
of standard errors (as described later in this chapter), you call the critical
value the z*-value (pronounced z-star value). See Table 13-1 for a list of
z*-values for some of the most common confidence levels.

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