AMDG

Name

Ms. Kresović

AP Statistics, 4th period

Tuesday 16 January 2012

Hiring discrimination: It just won’t fly!

An airline has just finished training 25 junior pilots – 15 male and 10 female – to become captains. Unfortunately, only eight captain positions are available right now. Airline managers announce that they will use a lottery process (random selection) to determine which pilots will fill the available positions. The names of all 25 pilots will be written on identical slips of paper, placed in a hat, mixed thoroughly, and drawn out one at a time until all eight captains have been identified.

A day later, managers announce the results of the lottery. Of the eight captains chosen, five are female and only three are male. Some of the male pilots who were not selected suspect that the lottery was not carried out fairly. One of the pilots knows that you are taking a statistics class, and come to you for advice. You offer to consult with your classmates and get back to him.The key question in this possible discrimination case seems to be: could these results have happened just by chance? Let’s find out.

STEP 1: State the problem or describe the random phenomenon. Define the key components.

  • What is the likelihood that a pool of 15 male and 10 female pilots would result in randomly selecting 5 women and 3 men for the 8 available captain positions?

STEP 2: State the assumptions.

  • Any card is equally likely to occur on each draw.
  • Draws are independent of each other, that is what happens on one draw will not influence the next.

STEP 3: Design the model.

  • This simulation will represent the count and gender of each of the pilots in this case.
  • Select 10 red cards to represent females, and 15 black cards to represent males. Shuffle thoroughly. Each card represents the identical slips of paper containing the pilot’s names that were placed in a hat and mixed thoroughly.
  • One draw of a card represents one name being drawn from a hat in the lottery.

STEP 4: Simulate many repetitions. Conduct many trials and record the observation of interest.

  • Without looking, draw a card – one at a time – until 8 cards are chosen.
  • Count the number of female pilots selected. Record this value on the table below.
  • Return the cards to the pile of 25, and shuffle thoroughly. Then repeat four more times so that you have a total of five simulated lottery results.

Individual Data: Class dot plot

Trial / 1 / 2 / 3 / 4 / 5
Number of females
0 / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8

When you have completed all of the repetitions, plot the number of females in each of your five trials on a class dot plot on the board. Copy the class’s dot plot on the table at right.

Discuss the results with your classmates.

Number of female pilots selected in

a simulated lottery with ____ trials.

Here are the results of 500 simulated repetitions of the airline lottery from Fathom software.

STEP 5: Summarize the information and draw conclusions.

  • Discuss: Do the results of this simulation change your opinion about whether the lottery could have been carried out fairly? Why or why not?
  • What would you tell the male pilot who contacted you? Be sure to explain your reasoning clearly and succinctly.
    Note: If it’s unlikely that these 8 were selected randomly, then we say that the finding is statistically significant (This concept is formally introduced in chapter 10.)