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Exhibit 6.3 Selection of data for z-test
is usually the case, but you are permitted to designate other differences if you are
hypothesizing a speciﬁc difference in the sample means. For example, consider the
situation in which management is willing to purchase the training, but only if it
results in some minimum increase in scores. The desired difference in scores could
be tested as the Hypothesized Mean Difference .
The variances for the variables can be estimated to be the variances of the sam-
ples, as long as the samples are greater than approximately 30 observations. Recall
earlier that I suggested that a sample size of at least 30 was advantageous—this
is why! We can also use the variance calculated for the entire population at SC
(Table 6.2—Total SC VAR
=
77.31) since it is available, but the difference in the
calculated z-statistics is very minor: z-statistic using the sample variance is 2.7375
and 2.7475 for the known variance of SC. Next, we choose an
value of 0.05, but
you may want to make this smaller if you want to be very cautious about rejecting
true null hypotheses. Finally, this test of hypothesis is known as a two-tail test since
we are not speculating on whether one speciﬁc sample mean will be greater than the
other mean. We are simply positing a difference in the alternative. This is important
in the application of a critical z-value for possible rejection of the null hypothe-
sis. In cases where you have evidence that one mean is greater than another, then a
one-tail test is appropriate. The critical z-values, z-Critical one-tail and z-Critical
two-tail , and p-values, P(Z<
α
z) two-tail , are provided when
the analysis is complete. These values represent our thresholds for the test.
=
z) one-tail and P(Z<
=
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