Page 251 - Statistics for Dummies

To calculate it, do the following:
. (Assume the population stan-
1. Calculate the sample means
dard deviations, and are given.) Let n and n represent the two
2
1
sample sizes (they need not be equal).
See Chapter 5 for these calculations.
.
2. Find the difference between the two sample means:
Because μ – μ is equal to 0 if H is true, it doesn’t need to be included
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2
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in the numerator of the test statistic. However, if the difference they are
testing is any value other than 0, you subtract that value in the numera-
tor of the test statistic.
3. Calculate the standard error using the following equation:
4. Divide your result from Step 2 by your result from Step 3.
Chapter 15: Commonly Used Hypothesis Tests: Formulas and Examples 235
To interpret the test statistic, add the following two steps to the list:
5. Look up your test statistic on the standard normal (Z-) distribution (see
the Z-table in the appendix) and calculate the p-value.
(See Chapter 14 for more on p-value calculations.)
6. Compare the p-value to your significance level, such as 0.05. If it’s less
than or equal to 0.05, reject H . Otherwise, fail to reject H .
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(See Chapter 14 for the details on significance levels.)
The conditions for using this test are that the two population standard
deviations are known and either both populations have a normal distribution
or both sample sizes are large enough for the Central Limit Theorem (see
Chapter 11).
For example, suppose you want to compare the absorbency of two brands
of paper towels (call the brands Stats-absorbent and Sponge-o-matic). You
can make this comparison by looking at the average number of ounces each
brand can absorb before being saturated. H says the difference between the
o
average absorbencies is 0 (nonexistent), and H says the difference is not 0.
a
In other words, one brand is more absorbent than the other. Using statistical
notation, you have H = μ – μ = 0 versus H = μ – μ ≠ 0. Here, you have no
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indication of which paper towel may be more absorbent, so the not-equal-to
alternative is the one to use (see Chapter 14).
Suppose you select a random sample of 50 paper towels from each brand
and measure the absorbency of each paper towel. Suppose the average
absorbency of Stats-absorbent (x ) for your sample is 3 ounces, and assume
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