28 INTRODUCTION TO BASIC CONCEPTS IN EXPERIMENTAL DESIGN

versus some unspecified alternative greater than 100. I£ the experimenter
can reject the hypothesis that 4 < 100 at x < .05 level of significance,
then he can reject any other hypothesis that g < 100 at a level of significance
x .05. The decision rule for this example can be stated as follows: If the
test statistic falls among the highest 5 percent of z's in a normal distribution
under H,, reject Hb; otherwise do not reject H,. M Ho is rejected, the
experimenter, in this example, decides in favor of H,.

We have stated the null and alternative hypotheses, decided on an
appropriate sample statistic and test statistic, and specified the level of
significance that will be used in the decision process. The final steps in
the hypothesis-testing procedure are to specify the size of the sample that
will be observed, obtain the sample, compute the sample statistic and test
statistic, and make a decision. Suppose that a random sample of n < 100
observations has been obtained from the population and that the mean
of this sample is egual to Y — 102. Is the deviation of this sample mean
from the predicted mean of 100 large enough to lead the experimenter to
reject the null hypothesis? The probability associated with obtaining a
sample mean as deviant as 102 if the true mean is 100 can be determined
from

X -u M2-100 20 ,,;

zn ASIA 15

and the cumulative normal probability table in Appendix D.3. According to
Appendix D.3, the probability associated with obtaining a sample mean of
102 if the true mean is 100 is approximately .09. According to the decision
rules outlined above, the null hypothesis is not rejected, because 09 > .05,
and therefore z does not fall in the region for rejection of Ho. The regions
for rejection or nonrejection of H, are illustrated in Figure 1.5-2. If the

Sampling
distribution
under Ho

a
100 101 102 | 103
a ———— Do not reject H Reject H, —-

Figure 1.5-2 Regions of the sampling distri-
bution of z that lead to rejection or nonrejection
of H, according to decision rules specified
previously.