- Choose a test statistic. This choice depends on the null hypothesis as well
as the measurement scale. - Summarize findings and state appropriate conclusions.
This section involves the final step of the process outlined above.5.3.1 Rejection Region
The most common approach is the formation of a decision rule. All possible
values of the chosen test statistic (in the repeated sampling context) are divided
into two regions. The region consisting of values of the test statistic for which
the null hypothesisH 0 is rejected is called therejection region. The values of the
test statistic comprising the rejection region are those values that are less likely
to occur if the null hypothesis is true, and the decision rule tells us to rejectH 0
if the value of the test statistic that we compute from our sample(s) is one of the
values in this region. For example, if a null hypothesis is aboutm, say
H 0 :m¼ 10then a good place to look for a test statistic forH 0 isx, and it is obvious that
H 0 should be rejected ifxis far away from ‘‘10’’, the hypothesized value ofm.
Before we proceed, a number of related concepts should be made clear:
One-Sided versus Two-Sided Tests In the example above, a vital question is:
Are we interested in the deviation ofxfrom 10 in one or both directions? If we
are interested in determining whethermis significantlydi¤erentfrom 10, we
would perform a two-sided test and the rejection region would be as shown in
Figure 5.3a. On the other hand, if we are interested in whethermis significantly
largerthan 10, we would perform a one-sided test and the rejection region
would be as shown in Figure 5.3b.
Figure 5.3 Rejection regions for (a) a two-sided test and (b) a one-sided test.SUMMARIES AND CONCLUSIONS 197