Are student-athletes at Division I universities poorer students than non-athletes? The National College Athlete Association (NCAA) measures the academic outcomes of student-athletes with the Graduation Success Rate (GSR) – the percentage of eligible athletes who graduate within six years of entering college. According to NCAA, the GSR for all scholarship athletes at Division I institutions is 63%. It is well known that the GSR for all students at Division I colleges is 60%. Suppose the NCAA report was based on a sample of 500 student-athletes, of which 315 graduated within six years. Is this sufficient information to conclude that the GSR for all scholarship athletes at Division I institutions differs from 60%? Test using a =.05. a. What is the parameter of interest? b. State the hypotheses. c. What test statistic will you use and why? Explain.
Are student-athletes at Division I universities poorer students than non-athletes? The National College Athlete Association (NCAA) measures the academic outcomes of student-athletes with the Graduation Success Rate (GSR) – the percentage of eligible athletes who graduate within six years of entering college. According to NCAA, the GSR for all scholarship athletes at Division I institutions is 63%. It is well known that the GSR for all students at Division I colleges is 60%. Suppose the NCAA report was based on a sample of 500 student-athletes, of which 315 graduated within six years. Is this sufficient information to conclude that the GSR for all scholarship athletes at Division I institutions differs from 60%? Test using a =.05. a. What is the parameter of interest? b. State the hypotheses. c. What test statistic will you use and why? Explain.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Table II
Normal Curve Areas
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
.0
.0000
.0040
.0080
.0120
.0160
.0199
.0239
.0279
.0319
.0359
.1
.0398
.0438
.0478
.0517
.0557
.0596
.0636
.0675
.0714
.0753
.2
.0793
.0832
.0871
.0910
.0948
.0987
.1026
.1064
.1103
.1141
.1517
.1879
.3
.1179
.1217
.1255
.1293
.1331
.1368
.1406
.1443
.1480
.4
.1554
.1591
.1628
.1664
.1700
.2054
.1736
.1772
.1808
.1844
.5
.1915
.1950
.1985
.2019
.2088
.2123
2157
2190
.2224
.2257
2291
.2324
2422
.2486
2357
.2673
.2967
.6
.2389
.2454
.2517
.2549
.7
.2704
.2580
.2881
.2611
.2642
2734
.2764
.2794
.2823
.3106
.3365
.2852
.8
.2910
.2939
.2995
.3023
.3051
.3078
.3133
.9
3159
3186
.3212
.3238
.3264
3289
.3315
.3340
.3389
1.0
.3413
.3438
.3461
.3485
.3508
.3531
.3554
.3577
3599
.3621
1.1
.3643
3665
.3686
.3708
3729
.3749
.3770
.3790
3810
.3830
.4015
.4177
.4319
.4441
.3944
3962
.3997
.4162
4306
1.2
.3849
3869
.3888
.3907
.3925
3980
.4032
4192
.4049
4207
4082
4236
4370
.4099
4251
.4131
.4279
1.3
.4066
.4115
.4147
1.4
4222
.4265
.4292
1.5
4332
4345
.4357
.4382
4394
.4406
.4418
.4429
1.6
4452
4463
.4474
.4484
.4495
.4505
.4515
.4525
.4535
.4545
.4582
.4664
.4732
1.7
4554
.4564
.4573
4591
4599
.4608
.4616
4625
.4633
.4686
.4706
1.8
1.9
2.0
.4641
.4649
.4656
.4671
4678
.4693
.4699
.4713
.4719
.4726
.4738
.4744
4750
.4756
4761
.4767
4772
4778
.4783
.4788
.4793
4798
.4803
.4808
4812
.4817
2.1
4821
.4826
4830
4834
.4838
.4842
.4850
4854
.4846
4881
.4857
2.2
4861
4864
.4868
4871
.4875
.4878
4887
.4884
.4911
.4890
2.3
.4893
4896
.4898
.4901
4904
.4906
.4909
.4913
.4916
4931
.4948
2.4
4918
.4920
4922
4934
.4936
4925
.4943
4927
4929
4932
2.5
.4938
.4940
.4941
.4945
.4946
.4949
4951
.4952
2.6
4953
.4955
.4956
4957
.4959
.4960
4961
.4962
4963
4964
2.7
.4965
.4966
.4967
.4968
4969
.4970
.4971
.4972
4973
.4974
.4977
4978
.4984
4980
4986
2.8
.4974
.4975
4976
.4977
4979
.4979
.4981
2.9
4981
4982
.4982
4983
.4984
4985
4985
.4986
3.0
.4987
.4987
.4987
.4988
.4988
.4989
4989
.4989
4990
.4990

Transcribed Image Text:Are student-athletes at Division I universities poorer students than non-athletes? The
National College Athlete Association (NCAA) measures the academic outcomes of
student-athletes with the Graduation Success Rate (GSR) – the percentage of eligible
athletes who graduate within six years of entering college. According to NCAA, the GSR
for all scholarship athletes at Division I institutions is 63%. It is well known that the GSR
for all students at Division I colleges is 60%. Suppose the NCAA report was based on a
sample of 500 student-athletes, of which 315 graduated within six years. Is this sufficient
information to conclude that the GSR for all scholarship athletes at Division I institutions
differs from 60%? Test using a =.05.
a. What is the parameter of interest?
b. State the hypotheses.
c. What test statistic will you use and why? Explain.
d. Calculate the value of the test statistic.
e. Rejection region:
f. Conclusion:
g. Construct a 95% confidence interval for the parameter of interest and interpret your
result.
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