Question

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 90% confidence interval for the mean salary of all basketball coaches in NCAA Division I. $ 1123855.9 Incorrect: Your answer is incorrect. 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 90% 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

Answer 1

Given that he 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 90% confidence interval for the mean salary of all basketball coaches in NCAA Division I.

Here we use one sample z-interval since sample size is > 30 .

90% confidence interval for mu is,

Xbar - E < mu < Xbar + E

where XBar is sample mean.

E is margin of error.

E = Zc * (sd / sqrt(n))

where Zc is critical value for normal distribution.

sd is standard deviation of the data.

n is sample size.

For 90% confidence Zc = 1.645 - (by using statistical table)

zc	1.645
Xbar	$1465752
sd	$1346046
n	62

E = 1.645* (1346046 / sqrt(62)) = $281184.5

90% confidence interval for mu is (1465752-281184.5, 1465752+ 281184.5).

90% confidence interval for mu is ($1184567, $1746936).

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 90% confidence interval using the remaining 61 salaries.

Now we can see that Mike Krzyzewski's salary is $72,33,976, We have to delete this observation and recalculate confidence interval.

E = 1.645*(1130666 / sqrt(61)) = $238120.5

zc	1.645
Xbar	1371191
sd	1130666
n	61
E	238120.5

90% confidence interval for mu is ($1133070, $1609311).