Question

This Excel file DI Basketball Graduation Rates shows the graduation rates for the men's and women's basketball teams that participated in recent NCAA division I men's and women's basketball tournaments. There are data for 67 men's teams and 63 women's teams since Princeton had teams in both tournaments but does not report graduation rates. Use the data to calculate a 90% confidence interval for ?M - ?F, the difference in the mean graduation rates for all division I men's and women's basketball teams. Do not waste time entering this data into a graphing calculator! Use Excel or Statcrunch! Use 2 decimal places in your answers. lower bound of confidence interval upper bound of confidence interval Select the choice below that correctly interprets the confidence interval. Since the interval is entirely negative, it appears that their is no significant difference between the DI women's basketball mean graduation rate and the DI men's basketball mean graduation rate. Since the interval contains zero we can conclude that both graduation rates are too low. Since the interval is entirely positive it appears that both men's and women's mean basketball graduation rates are higher than the graduation rate for the general student body. Since the interval is entirely negative, it appears that the DI men's basketball mean graduation rate is higher than the DI women's basketball mean graduation rate. Since the interval is entirely negative, it appears that the DI women's basketball mean graduation rate is higher than the DI men's basketball mean graduation rate.

NCAA Basketball Tournament Graduation Success Rate (GSR) of Participating* Men's and Women's Teams
* 67 men's teams and 63 women's teams since Princeton does not report graduation rates
School	Men/Women	Graduation Rate
Akron	men	38
Alabama State	men	63
Arizona	men	20
Arkansas-Little Rock	men	92
Belmont	men	100
Boston	men	90
Bucknell	men	91
Butler	men	83
BYU	men	100
Cincinnati	men	53
Clemson	men	71
Connecticut	men	31
Duke	men	83
Florida	men	44
Florida State	men	73
George Mason	men	67
Georgetown	men	78
Georgia	men	36
Gonzaga	men	73
Hampton	men	67
Illinois	men	100
Inidiana State	men	67
Kansas	men	80
Kansas State	men	40
Kentucky	men	44
Long Island	men	78
Louisville	men	50
Marquette	men	91
Memphis	men	58
Michigan	men	36
Michigan State	men	50
Missouri	men	44
Morehead State	men	43
North Carolina	men	88
Northern Colorado	men	77
Notre Dame	men	100
Oakland	men	75
Ohio State	men	64
Old Dominion	men	63
Penn State	men	86
Pittsburgh	men	64
Purdue	men	67
Richmond	men	83
San Diego State	men	58
St. John's	men	70
St. Peter's College	men	70
Syracuse	men	54
Temple	men	33
Tennessee	men	40
Texas	men	42
Texas A&M	men	64
UAB	men	25
UC Santa Barbara	men	77
UCLA	men	70
UNC Asheville	men	50
UNLV	men	67
USC	men	42
UT San Anotonio	men	50
Utah State	men	100
Vanderbilt	men	93
VCU	men	56
Villanova	men	100
Washington	men	44
West Virginia	men	71
Wisconsin	men	70
Wofford	men	100
Xavier	men	92
Arizona State	women	92
Baylor	women	88
Bowling Green	women	100
California State, Fresno	women	80
California, Davis	women	86
Connecticut	women	92
Dayton	women	100
DePau	women	92
Duke	women	100
Florida State	women	77
Gardner-Webb	women	100
Georgetown	women	91
Georgia	women	77
Georgia Tech	women	77
Gonzaga	women	94
Green Bay	women	92
Hampton	women	50
Houston	women	78
Iowa	women	100
Iowa State	women	100
James Madison	women	71
Kansas State	women	92
Kentucky	women	91
Louisiana Tech	women	56
Louisville	women	93
Marist	women	100
Marquette	women	92
Maryland	women	67
McNeese State	women	81
Miami	women	100
Michigan State	women	77
Middle Tennessee	women	85
Montana	women	83
Navy	women	94
North Carolina	women	100
Northern Iowa	women	10
Notre Dame	women	100
Ohio State	women	100
Oklahoma	women	92
Penn State	women	100
Prairie View A&M	women	57
Purdue	women	71
Rutgers	women	90
Samford University	women	100
South Dakota State	women	100
St. Francis (PA)	women	100
St. John's	women	100
Stanford	women	100
Stetson	women	67
Temple	women	71
Tennessee	women	100
Tennessee, Martin	women	86
Texas	women	79
Texas	women	65
Texas Tech	women	100
UALR	women	89
UCF	women	94
UCLA	women	93
University of Hartford	women	100
University of Utah	women	83
Vanderbilt	women	100
West Virginia	women	70
Xavier	women	100

Answer 1

It must be clear that population standard deviation is unknown, so we will be using student's t for the confidence interval calculation.

Using excel function STDEV.S and AVERAGE for sample standard deviation and mean, we get the folloing data for men and women

Sample size for men(n1) = 67 and sample size for women(n2) = 63

we know that the formula for confidence interval calculation is

CI =

From student's t distribution table, we can see that the value of t critical for 90% confidence level with

degree of freedom = n1+ n2 -2 = 67+63-2 = 128, is 1.66(rounded to two decimals)

putting given values, this gives us

CI =

or we can write it as

Lower limit = (66.2537-86.746) -5.4980 = -25.99

Upper limit = (66.2537-86.746) +5.4980 = -14.99

Here, it is clear that confidence interval is entirely which means it does not contain the zero, i.e. we can say that mean graduation rate for men is lower than mean graduation rate for women

so, correct option is "Since the interval is entirely negative, it appears that the DI women's basketball mean graduation rate is higher than the DI men's basketball mean graduation rate"