Database Reference
In-Depth Information
FIGURE 1.24
SPSS output for One-Sample T-test.
The p -value is thus given as 0.107. But, we do have a slight complication here.
You will note that the “Sig.” (i.e., p -value) is labeled “two-tailed.” But our hypothesis
test is one-tailed! See sidebar.
SIDEBAR: HOW MANY TAILS?
When the issue is a “not over” versus “over,” which is the case here (H0: true average of new design
not over 4.10, versus H1: true average of new design is over 4.10), or, less frequent in practice, a
“not under” versus “under” form of comparison, we refer to the hypothesis test as “one-tailed,”
because the “rejection values,” based on common sense, are in only ONE tail of the curve—here,
the tail some amount above 4.10.
Conversely, when we are testing whether a true mean equals a speciic value, versus is not equal
to that speciic value (e.g., H0: μ = 4.1 versus H1: μ ≠ 4.1), that is called a two-tailed test, since we
would reject H0 if X-bar is too much in the direction of either of the TWO tails.
In the two curves below, the irst one illustrates a one-tail (upper tail) test, while the second
curve illustrates a two-tailed test. In both cases, the shaded-in region is the region that rejects H0.
 
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