1. Section 1.2 Continued Discrimination in the Workplace: Inference through Simulation: Discussion

2.  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.

3.  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.

4.  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.

5.  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.

6.  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.

7.  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.

8.  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. CasesA’sB’sTotal Female7916 Male51015 Total121931

9.  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.

10.  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.