Section 1.2 Continued
Discrimination in the Workplace:
Inference through Simulation: Discussion

Average age 48.6

Ten workers were selected from 14, so to simulate this
we would:
 List the 14 ages and assign numbers 1-14.
 Select 10 different employees randomly from the group




using random integers.
Find the average of these 10 ages.
Repeat these steps many times.
Create a dot plot of the averages.
This can then be used to calculate the proportion or
probability of randomly selecting 10 employees of an
average age within a certain range.

The average was 48.6. 45 of 200 dots are above
48.6 for a proportion of 0.225.

Meaning that the probability of getting an
average age of 48.6 or higher in a single trial is
22.5%.

This evidence would not help support Mr. Martin’s case.
It would mean we would expect this to happen by
chance 22.5% of the time, which is a reasonable chance
and not a rare occurence.

Approximate dot plot:

Explain why we consider looking at the probability
(proportion) of a range of values instead of a specific value.
Each individual value may or may not even appear, so it is
difficult to estimate a probability at a specific value.

Create a classroom Dot Plot of your averages for each
repetition.
 Look at the Dot Plot: How many times did we get a
result of 58 or higher?
 Based on our simulation, what is the probability that
you would randomly get an average age of 58 or
higher?

 Probability: proportion of successes out of total trials in
the long run.

If Westvaco was truly unbiased by age would you
expect that they chose the people they did? Explain.

If we decided that the probability was high enough that
there was reasonable possibility that Westvaco could have
chosen those employees without bias, then they may be off
the hook.

However, if the probability was very low, we can say that it is
very unlikely that they chose those employees unbiased of
age.
 They may still have valid reasoning, but now the need for
an explanation is on them.

Our overall probability of getting a 3 person average age
of 58 or older for the day was about 2-6%. What does
this mean to us?
 If we truly selected 3 employees by some other means that did
not have anything to do with age, the average age would be 58
or higher approx. 4% of the time.
 In one round of layoffs, there is a 3-6% chance of having an
average age of 58 or higher.

Is that significant enough to support Mr. Martin’s case
for age discrimination?
 Note: It is typical for a court to require 0.025 or 2.5% or less for
it to be considered truly significant enough to reject that it
happened by chance.

What is some key information you can get
from summary tables?
 Actual counts of certain characteristics within
cases.
 Maybe most importantly, the proportions of
characteristics within cases.
Cases
A’s
B’s
Total
Female
7
9
16
Male
5
10
15
Total
12
19
31

Consider the following information:

The number of violent crimes in a particular city has risen
over the past 10 years; in 1995 the police documented 437
violent crimes, whereas in 2005 there were a total of 541
documented violent crimes.

Is this data sufficient to draw a reasonable conclusion
regarding the level of change in violent crime? Explain
 Not really…we don’t know the change in the population of the city.
 If we did, a proportion of violent crime to population would be useful.


Page 17 P4
Page 18 E9, E12, E13

On E9 you may use a Calculator simulation
instead of slips of paper.

Be sure to answer questions completely with
the context of the situation as the focus.