StatisticsChapter 1 Statistical Reasoning:Investigating a Claim of Discrimination

Section 1.2 ContinuedDiscrimination in the Workplace:

Inference through Simulation: Discussion

Practice 5 – a complete answer 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.

Practice 5 cont.

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.

Dot Plot from 1.2 Simulation 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.

1.2 Simulation Reporting

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.

1.2 Simulation Discussion 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.

Simulation/Dot plot Inference 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.

Summary Tables

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

Context and Type of Data

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.

1.2b Homework

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.