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In Depth Information

If we reject the null hypothesis that there is no difference in the average scores,

then we are deciding in favor of the training indeed leading to a difference in scores.

As before, the decision will be made on the basis of a statistic that is calculated

from the sample data, in this case the
z-Statistic
, which is then compared to a

critical value. The critical value incorporates the decision maker’s willingness to

commit an error by possibly rejecting a true null hypothesis. Alternatively, we can

use the p-value of the test and compare it to the level of signiﬁcance which we have

adopted—frequently assumed to be 0.05. The steps in this procedure are quite sim-

ilar to the ones we performed in the chi-square analysis, with the exception of the

statistic that is calculated, z rather than chi-square.

6.5.2 Is There a Difference in Scores for SC Non-Prisoners and

EB Trained SC Prisoners?

The procedure for the analysis is shown in Exhibits 6.2 and 6.3. Exhibit 6.2 shows

the
Data Analysis
dialogue box in the Analysis group of the Data ribbon used to

perform the z-Test. We begin data entry for the z-Test in Exhibit 6.3 by identi-

fying the range inputs, including labels, for the two samples: 36 SC non-prisoner

standard trained scores (E1:E37) and 36 SC prisoners that receive special training

(G1:G37). Next, the dialog box requires a hypothesized mean difference. Since we

are assuming there is
no
difference in the null hypothesis, the input value is 0. This

Exhibit 6.2
Data analysis tool for z-test

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