1. Determining Sample Size
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2. Sample Size Determination: µ
In estimating µ based on sample statistics, how large a sample do we need for the level of precision we want?
To determine the sample size we need, we must know the (1) desired precision and (2) σ.
e, the half-width of the confidence interval estimator is the precision with which we are estimating. e is also called sampling error.
Sample Size Determination

3. Sample Size Determination: µ
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We use e to solve for n:
If then
and so
Sample Size Determination

4. Example
Suppose σ=20 based upon previous studies. We would like to estimate the population mean within ±10 of its true value, at α=.05 (i.e., 95% confidence). What sample size should we take?
= 15.4
so, we need a sample size of at least 15.4, or n=16. We round UP, not down.
Sample Size Determination

5. Sample Size Determination: P
Similarly, taking e (precision) from formula for the half-width of a confidence interval estimator for P:
Q: If we are trying to estimate the population proportion, P, what do we use for P in this formula?
Sample Size Determination

6. Example: Political Poll
Suppose a pollster wants a maximum error of
e = .01 with 95% confidence.
We assume that variance is the highest possible, so we use P=.5. This is the way we ensure that sampling error will be within ±.01 of the true population Proportion.
Then,
n = = 9,604
That is a VERY large sample.
Sample Size Determination

7. Example: Political Poll
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Let’s try that again with e = .03.
n = = 1,067
This is the sample size that most pollsters work with.
Sample Size Determination

8. Homework Practice, practice, practice.
As always, do lots and lots of problems. You can find these in the online lecture notes and homework assignments.
Sample Size Determination