Page 221 - Statistics for Dummies

Chapter 13: Confidence Intervals: Making Your Best Guesstimate
In this formula, MOE is the number representing the margin of error you
want, and z* is the z*-value corresponding to your desired confidence level
(from Table 13-1; most people use 1.96 for a 95% confidence interval). If the
population standard deviation, , is unknown, you can put in a worst-case
scenario guess for it or run a pilot study (a small trial study) ahead of time,
find the standard deviation of the sample data (s), and use that number. This
can be risky if the sample size is very small because it’s less likely to reflect
the whole population; try to get the largest trial study that you can, and/or 205
make a conservative estimate for .
Often a small trial study is worth the time and effort. Not only will you get
an estimate of to help you determine a good sample size, but you may also
learn about possible problems in your data collection.
I only include one formula for calculating sample size in this chapter: the one
that pertains to a confidence interval for a population mean. (You can,
however, use the quick and dirty formula in the earlier section “Factoring in
the Sample Size” for handling proportions.)
Here’s an example where you need to calculate n to estimate a population
mean. Suppose you want to estimate the average number of songs college
students store on their portable devices. You want the margin of error to be
no more than plus or minus 20 songs. You want a 95% confidence interval.
How many students should you sample?

Because you want a 95% CI, z* is 1.96 (found in Table 13-1); you know your
desired MOE is 20. Now you need a number for the population standard devi-
ation, . This number is not known, so you do a pilot study of 35 students
and find the standard deviation (s) for the sample is 148 songs — use this
number as a substitute for . Using the sample size formula, you calculate the

sample size you need is , which you round
up to 211 students (you always round up when calculating n). So you need
to take a random sample of at least 211 college students in order to have a
margin of error in the number of stored songs of no more than 20. That’s why
you see a greater-than-or-equal-to sign in the formula here.

You always round up to the nearest integer when calculating sample size, no
matter what the decimal value of your result is (for example, 0.37). That’s
because you want the margin of error to be no more than what you stated. If
you round down when the decimal value is under .50 (as you normally do in
other math calculations), your MOE will be a little larger than you wanted.

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