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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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