Hypothesis Testing (In-state):
university_data <- read.table(textConnection("
University,Tuition,Salary,Ratio
'New Mexico Institute of Mining and Technology',16280,83700,5.141277641277641
'University of Texas at El Paso',13038,66350,5.088970701027765
'Utah State University',13824,69725,5.043764467592593
'University of Florida',16501,79475,4.816374765165747
'University of New Mexico',15309,71825,4.691684629956235
'Idaho State University',14627,67225,4.595952690230396
'University of Wyoming',15720,70550,4.487913486005089
'Western Carolina University',13902,61850,4.449000143864192
'University of Idaho',16744,71900,4.294075489727664
'Iowa State University',17708,74750,4.221255929523379
'New Mexico State University',16620,69900,4.205776173285199
'Oklahoma State University',17568,73500,4.183743169398907
'University of Central Florida',15985,66050,4.131998748827026
'University of North Dakota',17669,73000,4.131529797951214
'Purdue University',20022,82575,4.124213365298172
'Texas A&M University',21404,87025,4.065828817043543
'Appalachian State University',15518,62675,4.038858100270653
'Georgia Institute of Technology',24308,96625,3.975028797103834
'Florida State University',17332,68725,3.965208862220171
'South Dakota State University',16660,65975,3.9600840336134455
'Missouri State University',16207,63625,3.9257728142160793
'Florida International University',17440,68175,3.9091169724770642
'Southern Utah University',13859,54125,3.905404430334079
'North Dakota State University',17859,69675,3.9013942549974803
'University of Utah',19484,75750,3.887805378772326
'Mississippi State University',18850,72650,3.8541114
'East Carolina University', 16794, 64600, 3.846611885197094
'University of Montana', 16788, 64275, 3.828627591136526
'Tennessee Technological University', 18839, 72075, 3.82584001273953
'Virginia Polytechnic Institute and State University', 22554, 86075, 3.816396204664361
'Lamar University', 19112, 72875, 3.813049393051486
'North Carolina State University', 20179, 76825, 3.807175776797661
'Pittsburg State University', 15076, 57300, 3.8007429026266912
'University of Iowa', 20439, 76425, 3.739175106414208
'University of Arkansas', 20150, 75150, 3.729528535980149
'University of North Carolina at Charlotte', 18144, 67450, 3.7174823633156966
'University of Alabama at Birmingham', 17110, 63525, 3.7127410870835766
'Florida Atlantic University', 17935, 66550, 3.7106216894340673
'University of North Carolina at Chapel Hill', 20177, 74725, 3.70347425286217
'University of Mississippi', 19356, 70650, 3.6500309981401116
'University of South Florida', 18020, 65450, 3.6320754716981134
'West Virginia University', 19774, 70725, 3.5766663295236167
'University of Texas at Arlington', 20552, 73350, 3.5689957181782797
'Kansas State University', 19943, 70600, 3.5400892543749687
'San Jose State University', 24238, 85400, 3.523393019226009
'University of Georgia', 21868, 76475, 3.4971190781049937
'Western Washington University', 19598, 68500, 3.4952546178181447
'University of North Carolina at Wilmington', 17686, 61400, 3.471672509329413
'San Francisco State University', 22411, 77600, 3.4625853375574493
'Arkansas State University', 16768, 57800, 3.4470419847328246
'Fort Lewis College', 18918, 65200, 3.4464531134369385
'University of Kansas', 21498, 74050, 3.4445064657177413
'Boise State University', 18386, 61625, 3.3517350157728707
'Portland State University', 19533, 65050, 3.330261608559873
'University of Oklahoma', 22757, 75475, 3.316561936986422
'University of Illinois at Urbana-Champaign', 26402, 87475, 3.3131959700022726
'George Mason University', 23922, 78975, 3.301354401805869
'Washington State University', 22979, 75500, 3.285608599155751
'Bowling Green State University', 20273, 66175, 3.264193755240961
'Arizona State University', 23470, 76550, 3.261610566680869
'University of Memphis', 19676, 63425, 3.223470217523887
'Humboldt State University', 20546, 66150, 3.2196047892533826
'University of Toledo', 21229, 68275, 3.216119459230298
'University of Virginia', 29154, 93375, 3.202819510187281
'University of Michigan', 26796, 85775, 3.2010374682788476
'Northern Illinois University', 23142, 73900, 3.1933281479560973
'San Diego State University', 24223, 77300, 3.191181934525038
'Oregon State University', 24021, 76350, 3.1784688397652054
'University of Washington', 24315, 77225, 3.1760230310507915
'University of Houston', 22776, 72025, 3.162319985950123
'Michigan State University', 24782, 78025, 3.1484545234444354
'Eastern Washington University', 20116, 63275, 3.1455060648240205
'Evergreen State College', 19295, 60550, 3.1381186835967867
'University of Arizona', 25037, 78075, 3.1183847905100452
'University of Southern Maine', 18970, 59150, 3.1180811808118083
'Colorado State University', 23795, 73225, 3.0773271695734397
'Auburn University', 24608, 75450, 3.0660760728218466
'Colorado School of Mines', 32133, 98500, 3.065384495689789
'Georgia State University', 22236, 67750, 3.046860946213348
'Rutgers University', 27680, 83800, 3.027456647398844
'Western Michigan University', 22626, 67900, 3.0009723327145763
'Ball State University', 20130, 60275, 2.994287133631396
'Clemson University', 25802, 76800, 2.9765134485698783
'University of Texas at San Antonio', 21478, 63925, 2.9763013315951206
'University of Oregon', 24861, 73450, 2.9544266119625116
'University of Delaware', 26542, 78350, 2.951925250546304
'Wayne State University', 23774, 69025, 2.903381845713805
'University of Illinois at Chicago', 25838, 74500, 2.8833501044972523
'Union College', 30850, 88300, 2.8622366288492707
'Ohio University', 24022, 68600, 2.8557155940387977
'University of Kentucky', 25227, 71350, 2.8283188647084474
'Illinois State University', 24366, 68900, 2.827710744480013
'University of Connecticut', 28604, 80800, 2.8247797510837644
'Morehead State University', 19130, 53475, 2.795347621536853
'University of Rhode Island', 27088, 75325, 2.7807516243354993
'Tarleton State University', 20877, 57750, 2.766202040523064
'Austin Peay State University', 19111, 52825, 2.764114907644812
'University of Akron', 23663, 64975, 2.7458479482736764
'Cleveland State University', 24185, 66300, 2.7413686169113087
'Kent State University', 21374, 58525, 2.7381397960138485
'Eastern Michigan University', 23813, 65150, 2.7359005585184564
'Virginia Commonwealth University', 24918, 65575, 2.6316317521470425
'Southern Illinois University Carbondale', 25326, 66525, 2.626747216299455
'Union College', 34740, 88300, 2.5417386298215314
'University of Vermont', 30738, 76875, 2.50097599063049
'University of New Hampshire', 30079, 72625, 2.414475215266465
'Princeton University', 65620, 121875, 1.8572843645230113
'Thomas Aquinas College', 33400, 61675, 1.846556886227545
'Thomas Aquinas College', 33400, 61675, 1.846556886227545
'Dartmouth College', 71209, 129050, 1.8122709208105716
'Wentworth Institute of Technology', 48140, 85175, 1.769318653926049
'Massachusetts Institute of Technology', 67342, 116350, 1.7277479136348788
'California Institute of Technology', 67887, 115875, 1.7068805515047063
'Yale University', 69430, 115925, 1.6696672907964856
'University of Pennsylvania', 71200, 113025, 1.5874297752808988
'Harvey Mudd College', 75003, 117450, 1.5659373625054998
'Worcester Polytechnic Institute', 65304, 100800, 1.543550165380375
'Wittenberg University', 49856, 75625, 1.5168685815147624
'Siena College', 52575, 79525, 1.512601046124584
'Illinois Institute of Technology', 60058, 88050, 1.4660827866395818
'Cornell University', 70004, 102525, 1.46455916804754
'Washington and Lee University', 66380, 96600, 1.4552576077131667
'Colgate University', 69865, 101125, 1.4474343376511845
'Carnegie Mellon University', 69883, 100725, 1.4413376643818954
'Bucknell University', 69754, 100175, 1.4361183588037962
'Amherst College', 71166, 102100, 1.434673861113453
'Rensselaer Polytechnic Institute', 69140, 99150, 1.4340468614405555
'Stevens Institute of Technology', 67446, 96375, 1.4289209145093853
'Swarthmore College', 68062, 96975, 1.4248038553083953
'Randolph-Macon College', 53260, 75825, 1.423676304919264
'Brown University', 70326, 99650, 1.4169723857463812
'Lafayette College', 68520, 96050, 1.401780502043199
'Davidson College', 65819, 91650, 1.3924550661663047
'Bowdoin College', 68620, 93925, 1.368770037889828
'University of Richmond', 64860, 88400, 1.3629355534998457
'College of the Holy Cross', 67290, 91200, 1.355327686134641
'Columbia University', 74001, 99825, 1.3489682571857138
'Pomona College', 69496, 93475, 1.345041441234028
'Rochester Institute of Technology', 57176, 76900, 1.3449699174478802
'Williams College', 69950, 93275, 1.3334524660471765
'St. Olaf College', 58690, 78125, 1.331146703015846
'Bates College', 69018, 91625, 1.3275522327508766
'Occidental College', 70182, 92175, 1.3133709498161923
'Carleton College', 68844, 90225, 1.31057172738365
'Union College', 68853, 88300, 1.2824423046199875
'Juniata College', 58118, 74475, 1.281444647097285
'DePauw University', 62724, 80025, 1.2758274344748421
'Mount Holyoke College', 64658, 81150, 1.2550651118191098
'Gustavus Adolphus College', 55310, 68850, 1.2448020249502803
'Gettysburg College', 67490, 82200, 1.2179582160320048
'Middlebury College', 69980, 85000, 1.2146327522149185
'Denison University', 64670, 77400, 1.1968455234266275
'Wesleyan University', 69974, 83225, 1.1893703375539486
'Moravian College', 57014, 67125, 1.1773424071280738
'University of Puget Sound', 62316, 73050, 1.1722511072597728
'Colby College', 69400, 81175, 1.1696685878962536
'Whitman College', 64938, 74850, 1.1526379007668854
'Grinnell College', 65202, 75075, 1.151421735529585
'Vassar College', 70510, 81050, 1.149482342930081
'Colorado College', 67982, 77725, 1.1433173487099526
'Smith College', 69924, 79175, 1.132300783708026
'Hamilton College', 68490, 76950, 1.123521681997372
'Skidmore College', 68914, 76500, 1.1100792291842005
'Wellesley College', 70200, 77475, 1.1036324786324787
'Ursinus College', 64800, 69100, 1.066358024691358
'Lewis & Clark College', 63424, 67225, 1.0599299949545913
'Oberlin College', 71392, 74850, 1.0484367996414163
'Reed College', 70550, 72500, 1.0276399716513112
"), sep=",", header = TRUE, quote = "'")
# Calculate the median tuition
median_tuition <- median(university_data$Tuition)
print (median_tuition)## [1] 24340.5# Split the data into two groups
low_tuition_group <- university_data$Ratio[university_data$Tuition < median_tuition]
high_tuition_group <- university_data$Ratio[university_data$Tuition > median_tuition]
# Perform a two-sample t-test
t_test_result <- t.test(low_tuition_group, high_tuition_group, var.equal = FALSE)
# Output the result of the t-test
print(t_test_result)##
## Welch Two Sample t-test
##
## data: low_tuition_group and high_tuition_group
## t = 18.676, df = 157.83, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 1.655959 2.047639
## sample estimates:
## mean of x mean of y
## 3.619272 1.767473Hypothesis Testing (Out-of-State):
university_data <- read.table(textConnection("
University,Tuition,Salary,Ratio
'Western Carolina University',8220,61850,7.524330900243309
'Northern Illinois University',12262,73900,6.0267493068015
'South Dakota State University',12128,65975,5.439891160949868
'North Dakota State University',13273,69675,5.2493784374293675
'San Jose State University',17300,85400,4.936416184971098
'Eastern Michigan University',13959,65150,4.667239773622752
'Southern Illinois University Carbondale',14704,66525,4.524279107725789
'Cleveland State University',14992,66300,4.422358591248666
'Western Michigan University',15373,67900,4.4168347102062055
'Missouri State University',15342,63625,4.147112501629514
'San Francisco State University',19140,77600,4.054336468129572
'University of Wyoming',17490,70550,4.033733562035449
'San Diego State University',19368,77300,3.9911193721602642
'Morehead State University',13646,53475,3.918730763593727
'Arkansas State University',15298,57800,3.778271669499281
'University of South Florida',17324,65450,3.7779958439159547
'New Mexico Institute of Mining and Technology',22268,83700,3.7587569606610383
'Union College',23780,88300,3.7132043734230447
'University of Akron',17750,64975,3.66056338028169
'Florida International University',18956,68175,3.596486600548639
'University of Toledo',19133,68275,3.568441958919145
'University of North Dakota',20759,73000,3.5165470398381427
'Bowling Green State University',19093,66175,3.465929921960928
'Humboldt State University',19556,66150,3.382593577418695
'Fort Lewis College',19696,65200,3.3103168155970755
'University of North Carolina at Charlotte',20478,67450,3.2937786893251295
'Union College',27140,88300,3.253500368459838
'Utah State University',21505,69725,3.242269239711695
'Lamar University',22642,72875,3.218576097517887
'Iowa State University',23392,74750,3.1955369357045145
'Florida State University',21683,68725,3.169533736106627
'Ohio University',21656,68600,3.1677133357960843
'Kent State University',18714,58525,3.12733782195148
'Mississippi State University',23360,72650,3.110017123287671
'Florida Atlantic University',21595,66550,3.0817318823801805
'Pittsburg State University',18642,57300,3.0737045381396846
'Oklahoma State University',24539,73500,2.995232079546844
'University of Arkansas',25168,75150,2.9859345200254293
'New Mexico State University',23508,69900,2.973455844818785
'University of Memphis',21413,63425,2.961985709615654
'University of Texas at El Paso',22529,66350,2.9450929912557147
'University of Central Florida',22467,66050,2.9398673610183823
'Idaho State University',22940,67225,2.930470793374019
'Georgia Institute of Technology',33020,96625,2.9262568140520897
'University of Texas at Arlington',25134,73350,2.9183576032465983
'University of North Carolina at Wilmington',21065,61400,2.9147875623071444
'Western Washington University',23544,68500,2.9094461433910976
'University of Mississippi',24614,70650,2.870317705370927
'Purdue University',28794,82575,2.867784955199
'Washington State University',26365,75500,2.8636449838801443
'Appalachian State University',22021,62675,2.8461468598156303
'West Virginia University',24950,70725,2.8346693386773545
'University of Idaho',25500,71900,2.819607843137255
'Tennessee Technological University',25759,72075,2.7980511665825536
'University of Oklahoma',27144,75475,2.7805408193339227
'University of Florida',28658,79475,2.773222136925117
'University of Illinois at Urbana-Champaign',31664,87475,2.762601061141991
'University of Illinois at Chicago',26980,74500,2.761304670126019
'East Carolina University',23465,64600,2.7530364372469633
'Virginia Polytechnic Institute and State University',31304,86075,2.7496486072067468
'Kansas State University',25767,70600,2.7399386812589746
'University of Kansas',27358,74050,2.7067037064112873
'Arizona State University',28336,76550,2.7015104460756634
'North Carolina State University',28444,76825,2.700921108142315
'Tarleton State University',21412,57750,2.69708574631048
'Rutgers University',31282,83800,2.678856850585001
'University of New Mexico',26845,71825,2.675544794188862
'Illinois State University',26040,68900,2.6459293394777266
'University of Texas at San Antonio',24262,63925,2.634778666227022
'Southern Utah University',20585,54125,2.6293417537041535
'University of Southern Maine',22780,59150,2.59657594381036
'University of Utah',29215,75750,2.592846140681157
'Boise State University',23776,61625,2.591899394347241
'Eastern Washington University',24444,63275,2.5885697921780397
'University of Alabama at Birmingham',24630,63525,2.5791717417783193
'University of Houston',27956,72025,2.576370010015739
'University of Montana',24959,64275,2.575223366320766
'Colorado School of Mines',38584,98500,2.5528716566452414
'Oregon State University',30141,76350,2.5330944560565345
'University of Georgia',30404,76475,2.515294040257861
'Wentworth Institute of Technology',33950,85175,2.508836524300442
'Auburn University',30524,75450,2.4718254488271523
'Princeton University',49330,121875,2.4706061220352726
'Thomas Aquinas College',25000,61675,2.467
'Colorado State University',29732,73225,2.4628346562626127
'University of Kentucky',29099,71350,2.451974294649301
'University of Iowa',31233,76425,2.446931130535011
'Wayne State University',28241,69025,2.4441414964059347
'University of Rhode Island',30862,75325,2.4407037781090013
'Portland State University',27060,65050,2.4039172209903916
'Texas A&M University',36442,87025,2.388041271060864
'Dartmouth College',55453,129050,2.3271960038230572
'Georgia State University',29432,67750,2.3019162815982606
'Evergreen State College',26459,60550,2.2884462753694397
'University of Delaware',34310,78350,2.2835907898571843
'Ball State University',26468,60275,2.2772782227595587
'Massachusetts Institute of Technology',51832,116350,2.244752276585893
'California Institute of Technology',52362,115875,2.212959779993125
'George Mason University',35922,78975,2.1985134457992315
'Yale University',53430,115925,2.169661239004305
'Austin Peay State University',24467,52825,2.1590305309191975
'University of Arizona',36386,78075,2.145742868136096
'University of New Hampshire',33879,72625,2.1436583134094866
'University of North Carolina at Chapel Hill',35170,74725,2.124680125106625
'University of Connecticut',38098,80800,2.120846238647698
'Siena College',37575,79525,2.11643379906853
'University of Washington',36898,77225,2.0929318662258116
'Clemson University',36724,76800,2.091275460189522
'University of Oregon',35478,73450,2.070297085517786
'Harvey Mudd College',56876,117450,2.065018637034953
'University of Pennsylvania',55584,113025,2.0334088946459414
'Worcester Polytechnic Institute',50530,100800,1.994854541856323
'Michigan State University',39765,78025,1.9621526467999497
'University of Virginia',48465,93375,1.9266480965645312
'Wittenberg University',39500,75625,1.9145569620253164
'Virginia Commonwealth University',35138,65575,1.8662132164608116
'Illinois Institute of Technology',47296,88050,1.8616796346414073
'Cornell University',55188,102525,1.8577408132202653
'Stevens Institute of Technology',52202,96375,1.8461936324278763
'Swarthmore College',52588,96975,1.8440518749524606
'Washington and Lee University',52455,96600,1.8415784958535888
'Rensselaer Polytechnic Institute',53880,99150,1.8402004454342984
'Randolph-Macon College',41400,75825,1.8315217391304348
'Lafayette College',52880,96050,1.8163767019667172
'Carnegie Mellon University',55465,100725,1.8160100964572252
'Colgate University',55870,101125,1.8100053696080187
'Amherst College',56426,102100,1.8094495445362067
'University of Vermont',42516,76875,1.8081428168219023
'Brown University',55656,99650,1.7904628431795313
'Bucknell University',56092,100175,1.78590529843828
'Davidson College',51447,91650,1.7814449822147065
'Pomona College',52780,93475,1.7710306934444866
'Rochester Institute of Technology',44130,76900,1.7425787446181735
'Bowdoin College',53922,93925,1.7418678832387522
'University of Michigan',49350,85775,1.7380952380952381
'College of the Holy Cross',52770,91200,1.7282546901648663
'Bates College',53794,91625,1.7032568687957765
'Occidental College',54686,92175,1.6855319460190907
'Williams College',55450,93275,1.68214607754734
'University of Richmond',52610,88400,1.6802889184565672
'Columbia University',59985,99825,1.6641660415103776
'Carleton College',54759,90225,1.6476743549005644
'Juniata College',45597,74475,1.6333311402065926
'St. Olaf College',47840,78125,1.6330476588628762
'Mount Holyoke College',49998,81150,1.6230649225969038
'DePauw University',49704,80025,1.6100313858039594
'Union College',55290,88300,1.597033821667571
'Middlebury College',54450,85000,1.5610651974288339
'Moravian College',43636,67125,1.5382940691172426
'Gustavus Adolphus College',45400,68850,1.5165198237885462
'Wesleyan University',54914,83225,1.5155515897585314
'Smith College',52404,79175,1.5108579497748265
'Gettysburg College',54480,82200,1.5088105726872247
'Denison University',51960,77400,1.489607390300231
'Colby College',55210,81175,1.4702952363702229
'University of Puget Sound',49776,73050,1.4675747348119577
'Whitman College',51764,74850,1.4459856270767328
'Wellesley College',53732,77475,1.4418782103774288
'Grinnell College',52392,75075,1.4329477782867612
'Vassar College',56960,81050,1.4229283707865168
'Hamilton College',54620,76950,1.4088246063712926
'Skidmore College',54420,76500,1.4057331863285556
'Colorado College',55470,77725,1.401207860104561
'Oberlin College',55054,74850,1.3595742362044538
'Ursinus College',52050,69100,1.3275696445725265
'Lewis & Clark College',50934,67225,1.3198452899831155
'Reed College',56340,72500,1.2868299609513667
"), sep=",", header = TRUE, quote = "'")
# Calculate the median tuition
median_tuition <- median(university_data$Tuition)
print (median_tuition)## [1] 30404# Split the data into two groups
low_tuition_group <- university_data$Ratio[university_data$Tuition < median_tuition]
high_tuition_group <- university_data$Ratio[university_data$Tuition > median_tuition]
# Perform a two-sample t-test
t_test_result <- t.test(low_tuition_group, high_tuition_group, var.equal = FALSE)
# Output the result of the t-test
print(t_test_result)##
## Welch Two Sample t-test
##
## data: low_tuition_group and high_tuition_group
## t = 12.756, df = 110.45, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 1.147128 1.569106
## sample estimates:
## mean of x mean of y
## 3.232293 1.874176Confidence Interval (In-state):
university_data <- read.table(textConnection("
University,Tuition,Salary,Ratio
'New Mexico Institute of Mining and Technology',16280,83700,5.141277641277641
'University of Texas at El Paso',13038,66350,5.088970701027765
'Utah State University',13824,69725,5.043764467592593
'University of Florida',16501,79475,4.816374765165747
'University of New Mexico',15309,71825,4.691684629956235
'Idaho State University',14627,67225,4.595952690230396
'University of Wyoming',15720,70550,4.487913486005089
'Western Carolina University',13902,61850,4.449000143864192
'University of Idaho',16744,71900,4.294075489727664
'Iowa State University',17708,74750,4.221255929523379
'New Mexico State University',16620,69900,4.205776173285199
'Oklahoma State University',17568,73500,4.183743169398907
'University of Central Florida',15985,66050,4.131998748827026
'University of North Dakota',17669,73000,4.131529797951214
'Purdue University',20022,82575,4.124213365298172
'Texas A&M University',21404,87025,4.065828817043543
'Appalachian State University',15518,62675,4.038858100270653
'Georgia Institute of Technology',24308,96625,3.975028797103834
'Florida State University',17332,68725,3.965208862220171
'South Dakota State University',16660,65975,3.9600840336134455
'Missouri State University',16207,63625,3.9257728142160793
'Florida International University',17440,68175,3.9091169724770642
'Southern Utah University',13859,54125,3.905404430334079
'North Dakota State University',17859,69675,3.9013942549974803
'University of Utah',19484,75750,3.887805378772326
'Mississippi State University',18850,72650,3.8541114
'East Carolina University', 16794, 64600, 3.846611885197094
'University of Montana', 16788, 64275, 3.828627591136526
'Tennessee Technological University', 18839, 72075, 3.82584001273953
'Virginia Polytechnic Institute and State University', 22554, 86075, 3.816396204664361
'Lamar University', 19112, 72875, 3.813049393051486
'North Carolina State University', 20179, 76825, 3.807175776797661
'Pittsburg State University', 15076, 57300, 3.8007429026266912
'University of Iowa', 20439, 76425, 3.739175106414208
'University of Arkansas', 20150, 75150, 3.729528535980149
'University of North Carolina at Charlotte', 18144, 67450, 3.7174823633156966
'University of Alabama at Birmingham', 17110, 63525, 3.7127410870835766
'Florida Atlantic University', 17935, 66550, 3.7106216894340673
'University of North Carolina at Chapel Hill', 20177, 74725, 3.70347425286217
'University of Mississippi', 19356, 70650, 3.6500309981401116
'University of South Florida', 18020, 65450, 3.6320754716981134
'West Virginia University', 19774, 70725, 3.5766663295236167
'University of Texas at Arlington', 20552, 73350, 3.5689957181782797
'Kansas State University', 19943, 70600, 3.5400892543749687
'San Jose State University', 24238, 85400, 3.523393019226009
'University of Georgia', 21868, 76475, 3.4971190781049937
'Western Washington University', 19598, 68500, 3.4952546178181447
'University of North Carolina at Wilmington', 17686, 61400, 3.471672509329413
'San Francisco State University', 22411, 77600, 3.4625853375574493
'Arkansas State University', 16768, 57800, 3.4470419847328246
'Fort Lewis College', 18918, 65200, 3.4464531134369385
'University of Kansas', 21498, 74050, 3.4445064657177413
'Boise State University', 18386, 61625, 3.3517350157728707
'Portland State University', 19533, 65050, 3.330261608559873
'University of Oklahoma', 22757, 75475, 3.316561936986422
'University of Illinois at Urbana-Champaign', 26402, 87475, 3.3131959700022726
'George Mason University', 23922, 78975, 3.301354401805869
'Washington State University', 22979, 75500, 3.285608599155751
'Bowling Green State University', 20273, 66175, 3.264193755240961
'Arizona State University', 23470, 76550, 3.261610566680869
'University of Memphis', 19676, 63425, 3.223470217523887
'Humboldt State University', 20546, 66150, 3.2196047892533826
'University of Toledo', 21229, 68275, 3.216119459230298
'University of Virginia', 29154, 93375, 3.202819510187281
'University of Michigan', 26796, 85775, 3.2010374682788476
'Northern Illinois University', 23142, 73900, 3.1933281479560973
'San Diego State University', 24223, 77300, 3.191181934525038
'Oregon State University', 24021, 76350, 3.1784688397652054
'University of Washington', 24315, 77225, 3.1760230310507915
'University of Houston', 22776, 72025, 3.162319985950123
'Michigan State University', 24782, 78025, 3.1484545234444354
'Eastern Washington University', 20116, 63275, 3.1455060648240205
'Evergreen State College', 19295, 60550, 3.1381186835967867
'University of Arizona', 25037, 78075, 3.1183847905100452
'University of Southern Maine', 18970, 59150, 3.1180811808118083
'Colorado State University', 23795, 73225, 3.0773271695734397
'Auburn University', 24608, 75450, 3.0660760728218466
'Colorado School of Mines', 32133, 98500, 3.065384495689789
'Georgia State University', 22236, 67750, 3.046860946213348
'Rutgers University', 27680, 83800, 3.027456647398844
'Western Michigan University', 22626, 67900, 3.0009723327145763
'Ball State University', 20130, 60275, 2.994287133631396
'Clemson University', 25802, 76800, 2.9765134485698783
'University of Texas at San Antonio', 21478, 63925, 2.9763013315951206
'University of Oregon', 24861, 73450, 2.9544266119625116
'University of Delaware', 26542, 78350, 2.951925250546304
'Wayne State University', 23774, 69025, 2.903381845713805
'University of Illinois at Chicago', 25838, 74500, 2.8833501044972523
'Union College', 30850, 88300, 2.8622366288492707
'Ohio University', 24022, 68600, 2.8557155940387977
'University of Kentucky', 25227, 71350, 2.8283188647084474
'Illinois State University', 24366, 68900, 2.827710744480013
'University of Connecticut', 28604, 80800, 2.8247797510837644
'Morehead State University', 19130, 53475, 2.795347621536853
'University of Rhode Island', 27088, 75325, 2.7807516243354993
'Tarleton State University', 20877, 57750, 2.766202040523064
'Austin Peay State University', 19111, 52825, 2.764114907644812
'University of Akron', 23663, 64975, 2.7458479482736764
'Cleveland State University', 24185, 66300, 2.7413686169113087
'Kent State University', 21374, 58525, 2.7381397960138485
'Eastern Michigan University', 23813, 65150, 2.7359005585184564
'Virginia Commonwealth University', 24918, 65575, 2.6316317521470425
'Southern Illinois University Carbondale', 25326, 66525, 2.626747216299455
'Union College', 34740, 88300, 2.5417386298215314
'University of Vermont', 30738, 76875, 2.50097599063049
'University of New Hampshire', 30079, 72625, 2.414475215266465
'Princeton University', 65620, 121875, 1.8572843645230113
'Thomas Aquinas College', 33400, 61675, 1.846556886227545
'Thomas Aquinas College', 33400, 61675, 1.846556886227545
'Dartmouth College', 71209, 129050, 1.8122709208105716
'Wentworth Institute of Technology', 48140, 85175, 1.769318653926049
'Massachusetts Institute of Technology', 67342, 116350, 1.7277479136348788
'California Institute of Technology', 67887, 115875, 1.7068805515047063
'Yale University', 69430, 115925, 1.6696672907964856
'University of Pennsylvania', 71200, 113025, 1.5874297752808988
'Harvey Mudd College', 75003, 117450, 1.5659373625054998
'Worcester Polytechnic Institute', 65304, 100800, 1.543550165380375
'Wittenberg University', 49856, 75625, 1.5168685815147624
'Siena College', 52575, 79525, 1.512601046124584
'Illinois Institute of Technology', 60058, 88050, 1.4660827866395818
'Cornell University', 70004, 102525, 1.46455916804754
'Washington and Lee University', 66380, 96600, 1.4552576077131667
'Colgate University', 69865, 101125, 1.4474343376511845
'Carnegie Mellon University', 69883, 100725, 1.4413376643818954
'Bucknell University', 69754, 100175, 1.4361183588037962
'Amherst College', 71166, 102100, 1.434673861113453
'Rensselaer Polytechnic Institute', 69140, 99150, 1.4340468614405555
'Stevens Institute of Technology', 67446, 96375, 1.4289209145093853
'Swarthmore College', 68062, 96975, 1.4248038553083953
'Randolph-Macon College', 53260, 75825, 1.423676304919264
'Brown University', 70326, 99650, 1.4169723857463812
'Lafayette College', 68520, 96050, 1.401780502043199
'Davidson College', 65819, 91650, 1.3924550661663047
'Bowdoin College', 68620, 93925, 1.368770037889828
'University of Richmond', 64860, 88400, 1.3629355534998457
'College of the Holy Cross', 67290, 91200, 1.355327686134641
'Columbia University', 74001, 99825, 1.3489682571857138
'Pomona College', 69496, 93475, 1.345041441234028
'Rochester Institute of Technology', 57176, 76900, 1.3449699174478802
'Williams College', 69950, 93275, 1.3334524660471765
'St. Olaf College', 58690, 78125, 1.331146703015846
'Bates College', 69018, 91625, 1.3275522327508766
'Occidental College', 70182, 92175, 1.3133709498161923
'Carleton College', 68844, 90225, 1.31057172738365
'Union College', 68853, 88300, 1.2824423046199875
'Juniata College', 58118, 74475, 1.281444647097285
'DePauw University', 62724, 80025, 1.2758274344748421
'Mount Holyoke College', 64658, 81150, 1.2550651118191098
'Gustavus Adolphus College', 55310, 68850, 1.2448020249502803
'Gettysburg College', 67490, 82200, 1.2179582160320048
'Middlebury College', 69980, 85000, 1.2146327522149185
'Denison University', 64670, 77400, 1.1968455234266275
'Wesleyan University', 69974, 83225, 1.1893703375539486
'Moravian College', 57014, 67125, 1.1773424071280738
'University of Puget Sound', 62316, 73050, 1.1722511072597728
'Colby College', 69400, 81175, 1.1696685878962536
'Whitman College', 64938, 74850, 1.1526379007668854
'Grinnell College', 65202, 75075, 1.151421735529585
'Vassar College', 70510, 81050, 1.149482342930081
'Colorado College', 67982, 77725, 1.1433173487099526
'Smith College', 69924, 79175, 1.132300783708026
'Hamilton College', 68490, 76950, 1.123521681997372
'Skidmore College', 68914, 76500, 1.1100792291842005
'Wellesley College', 70200, 77475, 1.1036324786324787
'Ursinus College', 64800, 69100, 1.066358024691358
'Lewis & Clark College', 63424, 67225, 1.0599299949545913
'Oberlin College', 71392, 74850, 1.0484367996414163
'Reed College', 70550, 72500, 1.0276399716513112
"), sep=",", header = TRUE, quote = "'")
# Perform a one-sample t-test to get the confidence interval
t_test_result <- t.test(university_data$Ratio, conf.level = 0.95)
# The confidence interval is part of the t-test result
confidence_interval <- t_test_result$conf.int
# Output the confidence interval
print(confidence_interval)## [1] 2.521524 2.865220
## attr(,"conf.level")
## [1] 0.95# Perform a one-sample t-test to get the confidence interval
t_test_result <- t.test(university_data$Ratio, conf.level = 0.99)
# The confidence interval is part of the t-test result
confidence_interval <- t_test_result$conf.int
# Output the confidence interval
print(confidence_interval)## [1] 2.466572 2.920173
## attr(,"conf.level")
## [1] 0.99Confidence Interval (Out-of-State):
university_data <- read.table(textConnection("
University,Tuition,Salary,Ratio
'Western Carolina University',8220,61850,7.524330900243309
'Northern Illinois University',12262,73900,6.0267493068015
'South Dakota State University',12128,65975,5.439891160949868
'North Dakota State University',13273,69675,5.2493784374293675
'San Jose State University',17300,85400,4.936416184971098
'Eastern Michigan University',13959,65150,4.667239773622752
'Southern Illinois University Carbondale',14704,66525,4.524279107725789
'Cleveland State University',14992,66300,4.422358591248666
'Western Michigan University',15373,67900,4.4168347102062055
'Missouri State University',15342,63625,4.147112501629514
'San Francisco State University',19140,77600,4.054336468129572
'University of Wyoming',17490,70550,4.033733562035449
'San Diego State University',19368,77300,3.9911193721602642
'Morehead State University',13646,53475,3.918730763593727
'Arkansas State University',15298,57800,3.778271669499281
'University of South Florida',17324,65450,3.7779958439159547
'New Mexico Institute of Mining and Technology',22268,83700,3.7587569606610383
'Union College',23780,88300,3.7132043734230447
'University of Akron',17750,64975,3.66056338028169
'Florida International University',18956,68175,3.596486600548639
'University of Toledo',19133,68275,3.568441958919145
'University of North Dakota',20759,73000,3.5165470398381427
'Bowling Green State University',19093,66175,3.465929921960928
'Humboldt State University',19556,66150,3.382593577418695
'Fort Lewis College',19696,65200,3.3103168155970755
'University of North Carolina at Charlotte',20478,67450,3.2937786893251295
'Union College',27140,88300,3.253500368459838
'Utah State University',21505,69725,3.242269239711695
'Lamar University',22642,72875,3.218576097517887
'Iowa State University',23392,74750,3.1955369357045145
'Florida State University',21683,68725,3.169533736106627
'Ohio University',21656,68600,3.1677133357960843
'Kent State University',18714,58525,3.12733782195148
'Mississippi State University',23360,72650,3.110017123287671
'Florida Atlantic University',21595,66550,3.0817318823801805
'Pittsburg State University',18642,57300,3.0737045381396846
'Oklahoma State University',24539,73500,2.995232079546844
'University of Arkansas',25168,75150,2.9859345200254293
'New Mexico State University',23508,69900,2.973455844818785
'University of Memphis',21413,63425,2.961985709615654
'University of Texas at El Paso',22529,66350,2.9450929912557147
'University of Central Florida',22467,66050,2.9398673610183823
'Idaho State University',22940,67225,2.930470793374019
'Georgia Institute of Technology',33020,96625,2.9262568140520897
'University of Texas at Arlington',25134,73350,2.9183576032465983
'University of North Carolina at Wilmington',21065,61400,2.9147875623071444
'Western Washington University',23544,68500,2.9094461433910976
'University of Mississippi',24614,70650,2.870317705370927
'Purdue University',28794,82575,2.867784955199
'Washington State University',26365,75500,2.8636449838801443
'Appalachian State University',22021,62675,2.8461468598156303
'West Virginia University',24950,70725,2.8346693386773545
'University of Idaho',25500,71900,2.819607843137255
'Tennessee Technological University',25759,72075,2.7980511665825536
'University of Oklahoma',27144,75475,2.7805408193339227
'University of Florida',28658,79475,2.773222136925117
'University of Illinois at Urbana-Champaign',31664,87475,2.762601061141991
'University of Illinois at Chicago',26980,74500,2.761304670126019
'East Carolina University',23465,64600,2.7530364372469633
'Virginia Polytechnic Institute and State University',31304,86075,2.7496486072067468
'Kansas State University',25767,70600,2.7399386812589746
'University of Kansas',27358,74050,2.7067037064112873
'Arizona State University',28336,76550,2.7015104460756634
'North Carolina State University',28444,76825,2.700921108142315
'Tarleton State University',21412,57750,2.69708574631048
'Rutgers University',31282,83800,2.678856850585001
'University of New Mexico',26845,71825,2.675544794188862
'Illinois State University',26040,68900,2.6459293394777266
'University of Texas at San Antonio',24262,63925,2.634778666227022
'Southern Utah University',20585,54125,2.6293417537041535
'University of Southern Maine',22780,59150,2.59657594381036
'University of Utah',29215,75750,2.592846140681157
'Boise State University',23776,61625,2.591899394347241
'Eastern Washington University',24444,63275,2.5885697921780397
'University of Alabama at Birmingham',24630,63525,2.5791717417783193
'University of Houston',27956,72025,2.576370010015739
'University of Montana',24959,64275,2.575223366320766
'Colorado School of Mines',38584,98500,2.5528716566452414
'Oregon State University',30141,76350,2.5330944560565345
'University of Georgia',30404,76475,2.515294040257861
'Wentworth Institute of Technology',33950,85175,2.508836524300442
'Auburn University',30524,75450,2.4718254488271523
'Princeton University',49330,121875,2.4706061220352726
'Thomas Aquinas College',25000,61675,2.467
'Colorado State University',29732,73225,2.4628346562626127
'University of Kentucky',29099,71350,2.451974294649301
'University of Iowa',31233,76425,2.446931130535011
'Wayne State University',28241,69025,2.4441414964059347
'University of Rhode Island',30862,75325,2.4407037781090013
'Portland State University',27060,65050,2.4039172209903916
'Texas A&M University',36442,87025,2.388041271060864
'Dartmouth College',55453,129050,2.3271960038230572
'Georgia State University',29432,67750,2.3019162815982606
'Evergreen State College',26459,60550,2.2884462753694397
'University of Delaware',34310,78350,2.2835907898571843
'Ball State University',26468,60275,2.2772782227595587
'Massachusetts Institute of Technology',51832,116350,2.244752276585893
'California Institute of Technology',52362,115875,2.212959779993125
'George Mason University',35922,78975,2.1985134457992315
'Yale University',53430,115925,2.169661239004305
'Austin Peay State University',24467,52825,2.1590305309191975
'University of Arizona',36386,78075,2.145742868136096
'University of New Hampshire',33879,72625,2.1436583134094866
'University of North Carolina at Chapel Hill',35170,74725,2.124680125106625
'University of Connecticut',38098,80800,2.120846238647698
'Siena College',37575,79525,2.11643379906853
'University of Washington',36898,77225,2.0929318662258116
'Clemson University',36724,76800,2.091275460189522
'University of Oregon',35478,73450,2.070297085517786
'Harvey Mudd College',56876,117450,2.065018637034953
'University of Pennsylvania',55584,113025,2.0334088946459414
'Worcester Polytechnic Institute',50530,100800,1.994854541856323
'Michigan State University',39765,78025,1.9621526467999497
'University of Virginia',48465,93375,1.9266480965645312
'Wittenberg University',39500,75625,1.9145569620253164
'Virginia Commonwealth University',35138,65575,1.8662132164608116
'Illinois Institute of Technology',47296,88050,1.8616796346414073
'Cornell University',55188,102525,1.8577408132202653
'Stevens Institute of Technology',52202,96375,1.8461936324278763
'Swarthmore College',52588,96975,1.8440518749524606
'Washington and Lee University',52455,96600,1.8415784958535888
'Rensselaer Polytechnic Institute',53880,99150,1.8402004454342984
'Randolph-Macon College',41400,75825,1.8315217391304348
'Lafayette College',52880,96050,1.8163767019667172
'Carnegie Mellon University',55465,100725,1.8160100964572252
'Colgate University',55870,101125,1.8100053696080187
'Amherst College',56426,102100,1.8094495445362067
'University of Vermont',42516,76875,1.8081428168219023
'Brown University',55656,99650,1.7904628431795313
'Bucknell University',56092,100175,1.78590529843828
'Davidson College',51447,91650,1.7814449822147065
'Pomona College',52780,93475,1.7710306934444866
'Rochester Institute of Technology',44130,76900,1.7425787446181735
'Bowdoin College',53922,93925,1.7418678832387522
'University of Michigan',49350,85775,1.7380952380952381
'College of the Holy Cross',52770,91200,1.7282546901648663
'Bates College',53794,91625,1.7032568687957765
'Occidental College',54686,92175,1.6855319460190907
'Williams College',55450,93275,1.68214607754734
'University of Richmond',52610,88400,1.6802889184565672
'Columbia University',59985,99825,1.6641660415103776
'Carleton College',54759,90225,1.6476743549005644
'Juniata College',45597,74475,1.6333311402065926
'St. Olaf College',47840,78125,1.6330476588628762
'Mount Holyoke College',49998,81150,1.6230649225969038
'DePauw University',49704,80025,1.6100313858039594
'Union College',55290,88300,1.597033821667571
'Middlebury College',54450,85000,1.5610651974288339
'Moravian College',43636,67125,1.5382940691172426
'Gustavus Adolphus College',45400,68850,1.5165198237885462
'Wesleyan University',54914,83225,1.5155515897585314
'Smith College',52404,79175,1.5108579497748265
'Gettysburg College',54480,82200,1.5088105726872247
'Denison University',51960,77400,1.489607390300231
'Colby College',55210,81175,1.4702952363702229
'University of Puget Sound',49776,73050,1.4675747348119577
'Whitman College',51764,74850,1.4459856270767328
'Wellesley College',53732,77475,1.4418782103774288
'Grinnell College',52392,75075,1.4329477782867612
'Vassar College',56960,81050,1.4229283707865168
'Hamilton College',54620,76950,1.4088246063712926
'Skidmore College',54420,76500,1.4057331863285556
'Colorado College',55470,77725,1.401207860104561
'Oberlin College',55054,74850,1.3595742362044538
'Ursinus College',52050,69100,1.3275696445725265
'Lewis & Clark College',50934,67225,1.3198452899831155
'Reed College',56340,72500,1.2868299609513667
"), sep=",", header = TRUE, quote = "'")
# Perform a one-sample t-test to get the confidence interval
t_test_result <- t.test(university_data$Ratio, conf.level = 0.95)
# The confidence interval is part of the t-test result
confidence_interval <- t_test_result$conf.int
# Output the confidence interval
print(confidence_interval)## [1] 2.405997 2.700018
## attr(,"conf.level")
## [1] 0.95# Perform a one-sample t-test to get the confidence interval
t_test_result <- t.test(university_data$Ratio, conf.level = 0.99)
# The confidence interval is part of the t-test result
confidence_interval <- t_test_result$conf.int
# Output the confidence interval
print(confidence_interval)## [1] 2.358982 2.747033
## attr(,"conf.level")
## [1] 0.99