In: Statistics and Probability
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 |
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 =