Page 203 - Statistics for Dummies

Chapter 12: Leaving Room for a Margin of Error
The next time you hear a media story about a survey or poll that was con-
ducted, take a closer look to see if the margin of error is given; if it’s not, you
should ask why. Some news outlets are getting better about reporting the
margin of error for surveys, but what about other studies?
Calculating margin of error
for a sample mean
When a research question asks you to estimate a parameter based on a
numerical variable (for example, “What’s the average age of teachers?”), the
statistic used to help estimate the results is the average of all the responses
provided by people in the sample. This is known as the sample mean (or
average — see Chapter 5). And just like for sample proportions, you need to
report a MOE for sample means.
The general formula for margin of error for the sample mean (assuming a 187
certain condition is met) is , where σ is the population standard
deviation, n is the sample size, and z* is the appropriate z*-value for your
desired level of confidence (which you can find in Table 12-1).
Here are the steps for calculating the margin of error for a sample mean:
1. Find the population standard deviation, , and the sample size, n.
The population standard deviation will be given in the problem.
2. Divide the population standard deviation by the square root of the
sample size.
gives you the standard error.
3. Multiply by the appropriate z*-value (refer to Table 12-1).
For example, the z*-value is 1.96 if you want to be about 95% confident.
The condition you need to meet in order to use a z*-value in the margin of
error formula for a sample mean is either: 1) The original population has a
normal distribution to start with, or 2) The sample size is large enough so
the normal distribution can be used (that is, the Central Limit Theorem kicks
in; see Chapter 11). In general, the sample size, n, should be above about 30
for the Central Limit Theorem. Now, if it’s 29, don’t panic — 30 is not a magic
number, it’s just a general rule of thumb. (The population standard deviation
must be known either way.)

Suppose you’re the manager of an ice cream shop, and you’re training new
employees to be able to fill the large-size cones with the proper amount of

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