Question

In: Statistics and Probability

The attached Excel file 2013 NCAA BB Tournament shows the salaries paid to the coaches of...

The attached Excel file 2013 NCAA BB Tournament shows the salaries paid to the coaches of 62 of the 68 teams in the 2013 NCAA basketball tournament (not all private schools report their coach's salaries). Consider these 62 salaries to be a sample from the population of salaries of all 346 NCAA Division I basketball coaches.

Question 1. Use the 62 salaries from the TOTAL PAY column to construct a 99% confidence interval for the mean salary of all basketball coaches in NCAA Division I.

$ lower bound of confidence interval

$ upper bound of confidence interval

Question 2. Coach Mike Krzyzewski's high salary is an outlier and could be significantly affecting the confidence interval results. Remove Coach Krzyzewski's salary from the data and recalculate the 99% confidence interval using the remaining 61 salaries.

$lower bound of confidence interval

$ upper bound of confidence interval.

2013 NCAA Basketball Tournament: salaries of coaches (USA Today)
RANK SCHOOL CONF HEAD COACH SCHOOL PAY OTHER PAY TOTAL PAY MAX BONUS
1 Duke ACC Mike Krzyzewski $7,233,976 $0 $7,233,976 $0
2 Louisville Big East Rick Pitino $4,078,327 $895,016 $4,973,343 $725,000
3 Kansas Big 12 Bill Self $4,750,763 $210,000 $4,960,763 $525,000
4 Michigan State Big Ten Tom Izzo $3,220,769 $525,000 $3,745,769 $350,000
5 Florida SEC Billy Donovan $3,689,200 $0 $3,689,200 $471,500
6 Ohio State Big Ten Thad Matta $3,087,000 $107,000 $3,194,000 $410,000
7 Indiana Big Ten Tom Crean $2,886,250 $0 $2,886,250 $740,000
8 Arizona PAC-12 Sean Miller $2,100,000 $418,506 $2,518,506 $985,000
9 Wisconsin Big Ten Bo Ryan $2,100,000 $257,000 $2,357,000 $400,000
10 Villanova Big East Jay Wright $2,290,346 $0 $2,290,346 $0
11 Oklahoma State Big 12 Travis Ford $2,275,000 $0 $2,275,000 $0
12 UCLA PAC-12 Ben Howland $2,200,000 $50,000 $2,250,000 $235,000
13 Minnesota Big Ten Tubby Smith $2,215,769 $0 $2,215,769 $2,600,000
14 Georgetown Big East John Thompson $2,211,250 $0 $2,211,250 $0
15 Oklahoma Big 12 Lon Kruger $2,100,000 $0 $2,100,000 $270,000
16 North Carolina State ACC Mark Gottfried $1,950,000 $0 $1,950,000 $1,312,500
17 Syracuse Big East Jim Boeheim $1,905,576 $0 $1,905,576 $0
18 Michigan Big Ten John Beilein $1,800,000 $65,975 $1,865,975 $200,000
19 Pittsburgh Big East Jamie Dixon $1,830,176 $0 $1,830,176 $0
20 Oregon PAC-12 Dana Altman $1,800,000 $0 $1,800,000 $520,000
21 North Carolina ACC Roy Williams $1,773,938 $0 $1,773,938 $111,312
22 California PAC-12 Mike Montgomery $1,750,000 $6,500 $1,756,500 $350,000
23 Missouri SEC Frank Haith $1,650,000 $0 $1,650,000 $825,000
24 Gonzaga West Coast Mark Few $1,571,847 $0 $1,571,847 $0
25 Kansas State Big 12 Bruce Weber $1,500,000 $0 $1,500,000 $655,000
26 Illinois Big Ten John Groce $1,400,000 $0 $1,400,000 $775,000
27 Virginia Commonwealth A-10 Shaka Smart $1,370,000 $10,000 $1,380,000 $649,250
28 Creighton Mo. Valley Greg McDermott $1,369,949 $0 $1,369,949 $0
29 Cincinnati Big East Mick Cronin $1,350,000 $8,500 $1,358,500 $555,000
30 Mississippi SEC Andy Kennedy $1,300,000 $6,000 $1,306,000 $1,002,500
31 New Mexico Mt. West Steve Alford $1,209,200 $38,500 $1,247,700 $655,000
32 Memphis CUSA Josh Pastner $1,220,000 $0 $1,220,000 $545,000
33 Iowa State Big 12 Fred Hoiberg $1,200,000 $11,600 $1,211,600 $675,000
34 Wichita State Mo. Valley Gregg Marshall $1,155,000 $32,000 $1,187,000 $803,000
35 Butler A-10 Brad Stevens $1,165,940 $0 $1,165,940 $0
36 Marquette Big East Buzz Williams $1,105,203 $0 $1,105,203 $0
37 San Diego State Mt. West Steve Fisher $840,000 $17,500 $857,500 $185,000
38 Nevada-Las Vegas Mt. West Dave Rice $765,000 $954 $765,954 $345,000
39 Belmont Ohio Valley Rick Byrd $728,667 $0 $728,667 $0
40 Temple A-10 Fran Dunphy $724,557 $0 $724,557 $0
41 Notre Dame Big East Mike Brey $616,843 $0 $616,843 $0
42 Colorado PAC-12 Tad Boyle $591,310 $6,000 $597,310 $1,675,000
43 Saint Mary's West Coast Randy Bennett $517,381 $0 $517,381 $0
44 Colorado State Mt. West Larry Eustachy $500,000 $0 $500,000 $600,000
45 Boise State Mt. West Leon Rice $430,020 $10,500 $440,520 $75,500
46 New Mexico State WAC Marvin Menzies $423,868 $10,000 $433,868 $225,000
47 La Salle A-10 John Giannini $426,230 $0 $426,230 $0
48 Akron MAC Keith Dambrot $425,000 $1,000 $426,000 $723,167
49 Davidson Southern Bob McKillop $379,618 $0 $379,618 $0
50 Western Kentucky Sun Belt Ray Harper $375,000 $2,000 $377,000 $628,125
51 Pacific Big West Bob Thomason $322,651 $0 $322,651 $0
52 Liberty Big South Dale Layer $308,682 $0 $308,682 $0
53 Middle Tennessee State Sun Belt Kermit Davis $290,000 $14,000 $304,000 $80,000
54 James Madison CAA Matt Brady $290,000 $4,000 $294,000 $200,000
55 Albany Am East Will Brown $276,298 $17,000 $293,298 $202,700
56 Bucknell Patriot Dave Paulsen $222,389 $0 $222,389 $0
57 Montana Big Sky Wayne Tinkle $135,000 $43,500 $178,500 $146,000
58 Florida Gulf Coast Atl Sun Andrew Enfield $157,500 $2,050 $159,550 $95,000
59 South Dakota State Summit Scott Nagy $152,000 $1,025 $153,025 $17,000
60 North Carolina A&T MEAC Cy Alexander $150,000 $0 $150,000 $33,500
61 Northwestern State La Southland Mike McConathy $127,000 $0 $127,000 $16,000
62 Southern SWAC Roman Banks $115,000 $0 $115,000 $181,247

Solutions

Expert Solution

Question 1:

Mean of the Total Pay, mean, = 1465752. Standard Deviation, s = 1346046.

Confidence Interval (CI) = 99%. Then = 0.01.

Here n = 62. Then, Degress of Freedom = n - 1 = 61.

From the t distribution table (attached below) value of   2.658857.

Now,

So, the lower bound of CI, L =

So, the upper bound of CI, U =

Question 2:

After removing the salary of Mike Krzyzewski,

Mean of the Total Pay, mean, = 1371191. Standard Deviation, s = 1130666.

Confidence Interval (CI) = 99%. Then = 0.01.

Here n = 61. Then, Degress of Freedom = n - 1 = 60.

From the t distribution table (attached below) value of 2.660283.

Now,

So, the lower bound of CI, L =

So, the upper bound of CI, U =


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