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special training from EB. Additionally, the last two columns are the same individual
subjects, matched as before and after special training, respectively. The sample sizes
for the samples need not be the same, but it does simplify the analysis calculations.
Also, there are important advantages to samples greater than 30 observations that
we will discuss later.
Every customer service representative at the ﬁrm was tested at least once and
the SC women prisoners twice. Excel can easily store these sample data and pro-
vide access to speciﬁc data elements using the ﬁltering and sorting capabilities we
learned in Chap. 5. The data collected by EB provides us with an opportunity for
thorough analysis of the effectiveness of the special training.
So what are the questions of interest and how will we use inferential statistics to
answer them? Recall that EB administered special training to 36 women prisoners in
SC. We also have a standard trained non-prisoner group from SC. EB’s ﬁrst question
might be—Is there any difference between the average score of a randomly selected
SC non-prisoner sample with no special training and the SC prisoner’s average score
after special training? Note that our focus is on the aggregate statistic of average
scores for the groups. Additionally, EB’s question involves SC data exclusively. This
is done to not confound results, should there be a difference between the competency
of customer service representatives in TX and SC. We will study the issue of the
possible difference between Texas and SC scores later in our analysis.
6.5.1 z-Test: 2 Sample Means
To answer the question of whether or not there is a difference between the aver-
age scores of SC non-prisoners without special training and prisoners with special
training, we use the z-Test: Two Sample for Means option found in Excel’s Data
Analysis tool. This analysis tests the null hypothesis that there is no difference
between the two sample means and is generally reserved for samples of 30 obser-
vations or more. Pause for a moment to consider this statement. We are focusing
on the question of whether two means from sample data are different; different
in statistics suggests that the samples come from different underlying populations
with different means. For our problem, the question is whether the SC non-prisoner
group and the SC prisoner group with special training have different population
means for their scores. Of course, the process of calculating sample means will
very likely lead to different values. If the means are relatively close to one another,
then we will conclude that they came from the same population; if the means are
relatively different, we are likely to conclude that they are from different popu-
lations. Once calculated, the sample means will be examined and a probability
estimate will be made as to how likely it is that the two sample means came from
the same population. But the question of importance in these tests of hypothesis is
related to the populations—are the averages of the population of SC non-prisoners
and of the population of SC prisoners with special training the same, or are they
different?
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