Spring 2013
Math 263
Deb Hughes Hallett
Math 263: Excel Assignment 3 on Sampling Distributions:
Hiring Coaches in Football and Basketball
Purpose of Assignment: Sampling Distributions
We are about to start statistical inference, which means drawing conclusions about a population from a
sample. The central idea is that of a sampling distribution, which involves all the samples of a fixed size
from a population. This distribution allows us to decide whether a sample result is surprising. This
assignment is intended to get you to think (hard!) about sampling distributions.
The example we consider is the hiring of minority head coaches in universities. You will look at two
simulations (computer experiments) of random samples drawn from applicant pools similar to actual pools.
These simulations are approximations to sampling distributions. The assignment does not involve much
calculation; the purpose is for you to see how to draw conclusions from the data.
We will look at the hiring in two sports:1
 Men’s football, FBS (Division I-A), 2007-2008
 Women’s basketball, FBS (Division I), 2008-2009
For each sport, you will look at the data in the CoachSimulation.xlsx to decide whether roughly the
expected numbers of minority coaches were hired. To do this we must make some assumptions—in
particular, that all the candidates for a position are equally qualified. The table below shows the actual
data for the head coach positions.
Men’s Football, 07-08
Women’s Basketball, 08-09
Short-Listed
Candidates
74
55
Minority Short-Listed
Candidates
25
21
Positions
Available
18
16
Minorities
Hired
2
9
The spreadsheet has four pages, two for men and two for women. (One Live and one Frozen page.) For
each sport, there are some questions to be answered using the table above, some questions about the Live
page, and some questions about the Frozen page.
MEN’S FOOTBALL
Prior Expectations
1. Given the number of minority candidates for men’s football, how many minority coaches would you
have expected to be hired for the 18 available positions? (Assume all short-listed candidates were
equally qualified.)
1Idea from Tisha Hook and Chris Malone, Winona State University. Based on “Who you Know and Who Knows You: The Hiring Process and
Practice of NCAA FBS & FCS Head Coaching Positions” by K. Harrison et al, report for BCA (Black Coaches and Administrators) and “BCA
Hiring Report Card for Women’s College Basketball, 2008-2009” by R. Lapchick.
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Spring 2013
Math 263
Deb Hughes Hallett
2. Would you expect the number of minorities hired to be exactly the number you gave as your answer to
#1? Why or why not?
3. If the number of minority coaches hired was roughly as expected from the short-listed applicant pool,
is it likely, or unlikely, that two minority coaches were hired? Why?
Men’s Simulation: Live Page of Spreadsheet
4. The candidates are listed on the left. Press F9 (PC) or Apple+ (Mac) to see the sheet recalculate. The
big block in the middle shows many samples from the candidate pool. The result of each sample is
shown in the yellow column on the right. The result from all the samples is shown in the yellow rows
across the top.
(a) How many individuals were in each sample? Why was this number chosen?
(b) How many samples were taken?
(c) What do the numbers represent in the yellow column on the right (Column X)?
(d) What do the numbers represent in the yellow rows at the top (Rows 1 and 2)?
5. Compare the numbers in the yellow Row 2 with what you expected in #1. Are they what you expected
or not?
Men’s Simulation: Frozen Page of Spreadsheet
6. The data from the live simulation has been “frozen” so it will no longer recalculate, and a bar chart
made of the results. Based on this chart, estimate the probability that two minority coaches were hired.
7. Explain in words what the your answer to #6 tells us about whether the actual hiring of minority head
coaches in men’s football was as expected.
WOMEN’S BASKETBALL
Prior Expectations
8. Given the number of minority candidates for women’s basketball, how many minority coaches would
you have expected to be hired? (Assume all short-listed candidates were equally qualified.)
9. If the number of minority coaches hired was roughly as expected from the short-listed applicant pool,
is it likely, or unlikely, that nine minority coaches were hired? Is it more or less likely that 2 minority
men were hired?
Women’s Simulation: Live Page
10. How many individuals were in each sample? Why is it different than for the men’s simulation?
Women’s Simulation: Frozen Page
11. Based on the chart made from “frozen” data, estimate the probability that exactly nine minority
coaches were hired.
12. Explain in words what the your answer to #11 tells us about whether the actual hiring of minority head
coaches in women’s basketball was as expected?
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