An airline has just finished training 25 pilots15 male and 10 femaleto become captains.Unfortunately,only eight captain positions are available right now.Airline managers announce that they will use a lottery to determine which pilots will fill the available positions.The names of all 25 pilots will be written on identical slips of paper,which will be 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 8 captains chosen,5 are female and 3 are male.Some of the male pilots who weren't selected suspect that the lottery was not carried out fairly.One of these pilots asks your statistics class for advice about whether to file a grievance with the pilots' union. The key question in this possible discrimination case seems to be:is it plausible (believable) that these results happened just by chance?

Lab Directions & Prompts:

Pre-lab Questions:

1. If the drawing of names was truly fair, how many female pilots' names would you expect to be drawn? Explain your response.

1. In the lottery, 5 female and 3 male names were drawn. Do you feel like this is a reasonable result if the lottery is truly fair?

• Now, click the Next button at the top of the preview screen. Perform a simulation.

Lab Questions:

1. Record the gender breakdown of the randomly selected 8 pilots from four trials.

	Trial 1	Trial 2	Trial 3	Trial 4
Female	4	2	1	2
Male	4	6	7	6

1. Based on the simulation, do you feel like this is a reasonable result if the lottery is truly fair? Explain your thinking.

• Now, click the Next button at the top of the preview screen.Perform the simulation 50 times (Each time you press the Simulate button, the counts will update.)

1. In what proportion of your simulation trials were 5 or more females selected? [Perform the calculation:Trials with 5 or More Females count / Trials Completed Count...which should be 50.]

**5 out of 50 had 5 or more women**

1. In the lottery, 5 female and 3 male names were drawn. Based on the simulation with 50 trials, do you feel like this is a reasonable result if the lottery is truly fair? Explain your thinking. In other words, based on the results of 50 trials what would be the expected number of women and men selected to hired. Is this in line, closely enough, to 5 females and 3 males.

• Now, click the Next button at the top of the preview screen. Press Simulate once (it is in the upper right corner of the graph).

1. Take a photo, screenshot, or sketch the results.