Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

SECTION 8.1 | The Logic of Hypothesis Testing 231
normal table. In most cases, the distribution of sample means is normal, and the unit
normal table provides the precise z-score location for the critical region boundaries. With
α = .05, for example, the boundaries separate the extreme 5% from the middle 95%.
Because the extreme 5% is split between two tails of the distribution, there is exactly 2.5%
(or 0.0250) in each tail. In the unit normal table, you can look up a proportion of 0.0250
in column C (the tail) and find that the z-score boundary is z = 1.96. Thus, for any normal
distribution, the extreme 5% is in the tails of the distribution beyond z = +1.96 and
z = –1.96. These values define the boundaries of the critical region for a hypothesis test
using α = .05 (Figure 8.5).
Similarly, an alpha level of α = .01 means that 1% or .0100 is split between the two
tails. In this case, the proportion in each tail is .0050, and the corresponding z-score boundaries
are z = ±2.58 (±2.57 is equally good). For α = .001, the boundaries are located at
z = ±3.30. You should verify these values in the unit normal table and be sure that you
understand exactly how they are obtained.
STEP 3
Collect data and compute sample statistics. At this time, we begin recording tips
for male customers while the waitresses are wearing red. Notice that the data are collected
after the researcher has stated the hypotheses and established the criteria for a decision.
This sequence of events helps ensure that a researcher makes an honest, objective evaluation
of the data and does not tamper with the decision criteria after the experimental outcome
is known.
Next, the raw data from the sample are summarized with the appropriate statistics: For
this example, the researcher would compute the sample mean. Now it is possible for the
researcher to compare the sample mean (the data) with the null hypothesis. This is the heart
of the hypothesis test: comparing the data with the hypothesis.
The comparison is accomplished by computing a z-score that describes exactly where
the sample mean is located relative to the hypothesized population mean from H 0
. In Step 2,
we constructed the distribution of sample means that would be expected if the null
Reject H 0 Reject H 0
Middle 95%:
High-probability values
if H 0 is true
15.8
m from H 0
FIGURE 8.5
The critical region (very
unlikely outcomes) for
α = .05.
z 5 21.96 0
z 5 1.96
Critical region:
Extreme 5%