The data is from 80 universities and colleges. While we might assume tuition is higher at private institutions, one might not have any real reason to assume room and board is higher. Perform the appropriate statistical tests to determine if there is a significant difference in mean room and board costs between private and public institutions and state a clear conclusion in non-statistical language. State your null and alternative hypotheses Calculate or highlight the appropriate test statistic in the output
The data is from 80 universities and colleges. While we might assume tuition is higher at private institutions, one might not have any real reason to assume room and board is higher. Perform the appropriate statistical tests to determine if there is a significant difference in mean room and board costs between private and public institutions and state a clear conclusion in non-statistical language. State your null and alternative hypotheses Calculate or highlight the appropriate test statistic in the output
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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The data is from 80 universities and colleges.
- While we might assume tuition is higher at private institutions, one might not have any real reason to assume room and board is higher. Perform the appropriate statistical tests to determine if there is a significant difference in mean room and board costs between private and public institutions and state a clear conclusion in non-statistical language.
- State your null and alternative hypotheses
- Calculate or highlight the appropriate test statistic in the output
- Highlight the p-value or critical value comparison to determine the conclusion of the test
- Make a clear concluding statement without using the words reject or hypothesis.
Copy and paste the highlighted output
Make a clear conclusion about room and board between private and public schools.
If there is a significant difference in mean R&B costs, then construct the appropriate confidence
| School | Type of Term | Location | Type of School | Average Total SAT | TOEFL Score | Room and Board | Annual Total Cost | Average Indebtedness |
| ArizonaStateUniversity | 1 | 2 | 0 | 1080 | 0 | 4.3 | 12.7 | 12.9 |
| BallStateUniversity | 1 | 1 | 0 | 985 | 1 | 4 | 12.5 | 8.21 |
| Cal.StateUniv.-Fresno | 1 | 1 | 0 | 955 | 0 | 5.4 | 13.1 | 8.761 |
| ClemsonUniversity | 1 | 3 | 0 | 1130 | 1 | 3.9 | 12.4 | 9.983 |
| CollegeofWilliam&Mary | 1 | 2 | 0 | 1295 | 1 | 4.5 | 19.4 | 13.424 |
| FloridaInternationalUniv. | 1 | 1 | 0 | 1135 | 0 | 2.7 | 10 | 4.139 |
| FloridaStateUniversity | 1 | 1 | 0 | 1180 | 1 | 4.5 | 11.5 | 16.5 |
| GeorgeMasonUniversity | 1 | 2 | 0 | 1055 | 1 | 5 | 17 | 13 |
| GeorgiaStateUniversity | 0 | 1 | 0 | 1115 | 0 | 7.4 | 15.4 | 8.08 |
| MontclairStateUniversity | 1 | 2 | 0 | 1025 | 0 | 5.3 | 10.2 | 4.5 |
| NorthCarolinaStateUniv. | 1 | 1 | 0 | 1145 | 1 | 4 | 14.3 | 14.991 |
| OregonStateUniversity | 0 | 1 | 0 | 1072 | 1 | 4.4 | 15.5 | 10.5 |
| PurdueUniversity | 1 | 1 | 0 | 1095 | 1 | 4.5 | 15.2 | 11.839 |
| SanDiegoStateUniversity | 1 | 1 | 0 | 945 | 1 | 6.2 | 13.6 | 6.75 |
| SlipperyRockUniv.ofPenn. | 1 | 3 | 0 | 955 | 0 | 3.6 | 12.9 | 17 |
| SUNY-Binghamton | 1 | 2 | 0 | 1039 | 1 | 4.6 | 13.4 | 6.245 |
| TexasA&MUniversity | 1 | 1 | 0 | 1150 | 1 | 3.9 | 12.7 | 14.1 |
| Univ.ofGeorgia | 0 | 1 | 0 | 1180 | 1 | 4 | 11.9 | 10.8 |
| Univ.ofHawaii-Manoa | 1 | 1 | 0 | 1075 | 0 | 4.7 | 12.6 | 3.617 |
| Univ.ofHouston | 1 | 1 | 0 | 1065 | 1 | 4.1 | 12.1 | 9.404 |
| Univ.ofMaryland | 1 | 2 | 0 | 1170 | 1 | 5.5 | 15.7 | 16.637 |
| Univ.ofMass.-Amherst | 1 | 2 | 0 | 1100 | 1 | 4.2 | 16.4 | 10.2 |
| Univ.ofNevada-LasVegas | 1 | 1 | 0 | 980 | 0 | 5.5 | 12.3 | 10 |
| Univ.ofNewHampshire | 1 | 3 | 0 | 1110 | 1 | 4.4 | 18.6 | 9.66 |
| Univ.ofNorthCarolina-C.H. | 1 | 1 | 0 | 1225 | 1 | 4.5 | 15.2 | 9.406 |
| Univ.ofTexas-Austin | 1 | 1 | 0 | 1215 | 1 | 3.9 | 12.9 | 10.2 |
| Univ.ofVermont | 1 | 1 | 0 | 1115 | 1 | 5.1 | 22.4 | 21.5 |
| VirginiaCommonwealthUniv. | 1 | 1 | 0 | 1005 | 1 | 4.3 | 16.3 | 14.73 |
| VirginiaTech | 1 | 3 | 0 | 1265 | 1 | 3.5 | 14.9 | 10.327 |
| WestVirginiaUniversity | 1 | 1 | 0 | 1025 | 1 | 4.6 | 11.7 | 10.7 |
| BabsonCollege | 1 | 2 | 1 | 1165 | 1 | 7.6 | 26.4 | 18 |
| BostonCollege | 1 | 2 | 1 | 1285 | 1 | 7.5 | 26.8 | 15.855 |
| BostonUniversity | 1 | 1 | 1 | 1235 | 1 | 7 | 27.9 | 14.463 |
| BowdoinCollege | 1 | 2 | 1 | 1345 | 1 | 6 | 27.8 | 13.64 |
| BryantCollege | 0 | 2 | 1 | 1080 | 1 | 6.7 | 20.6 | 18 |
| BucknellUniversity | 1 | 3 | 1 | 1255 | 1 | 5 | 25.4 | 12.5 |
| CanisiusCollege | 1 | 1 | 1 | 1143 | 0 | 5.9 | 18.8 | 14.824 |
| CarnegieMellonUniversity | 1 | 1 | 1 | 1335 | 1 | 6.1 | 25.6 | 15.683 |
| CaseWesternReserveUniv. | 1 | 1 | 1 | 1330 | 1 | 5 | 22.2 | 26.031 |
| ClarkUniversity | 1 | 1 | 1 | 1121 | 1 | 4.4 | 24.4 | 17.5 |
| ColbyCollege | 0 | 1 | 1 | 1275 | 1 | 5.7 | 27.9 | 11.63 |
| ColgateUniversity | 1 | 3 | 1 | 1300 | 1 | 5.9 | 27.6 | 9.236 |
| CollegeofHolyCross | 1 | 1 | 1 | 1275 | 1 | 6.7 | 26.8 | 12.634 |
| EmoryUniversity | 1 | 1 | 1 | 1310 | 1 | 6.5 | 26.6 | 15.309 |
| FordhamUniversity | 1 | 1 | 1 | 1150 | 1 | 7.4 | 23.4 | 8.593 |
| Franklin&MarshallCollege | 1 | 1 | 1 | 1260 | 1 | 4.5 | 26.4 | 11.5 |
| GeorgeWashingtonUniversity | 1 | 1 | 1 | 1235 | 1 | 6.9 | 26.7 | 14.368 |
| GeorgetownUniversity | 1 | 1 | 1 | 1330 | 1 | 7.5 | 27.5 | 14.013 |
| GettysburgCollege | 1 | 3 | 1 | 1200 | 1 | 4.8 | 26.4 | 11.75 |
| HarvardUniversity | 1 | 1 | 1 | 1465 | 1 | 7 | 28.9 | 11.65 |
| IonaCollege | 1 | 2 | 1 | 955 | 1 | 7.3 | 19.8 | 18 |
| LafayetteCollege | 1 | 1 | 1 | 1185 | 1 | 6.3 | 26.7 | 11.499 |
| LaSalleUniversity | 1 | 1 | 1 | 1105 | 0 | 6.7 | 20.8 | 11.7 |
| LehighUniversity | 1 | 1 | 1 | 1225 | 1 | 6 | 26.8 | 13.84 |
| ManhattanCollege | 1 | 1 | 1 | 952 | 1 | 7.1 | 22 | 9.268 |
| NewYorkUniversity | 1 | 1 | 1 | 1260 | 1 | 7.8 | 28.6 | 17.318 |
| NiagaraUniversity | 1 | 2 | 1 | 1065 | 0 | 5.4 | 17.6 | 11.577 |
| NortheasternUniversity | 0 | 1 | 1 | 1055 | 1 | 8.2 | 23.4 | 25.603 |
| NorthwesternUniversity | 0 | 2 | 1 | 1350 | 1 | 6.1 | 24.2 | 11.98 |
| ProvidenceCollege | 1 | 1 | 1 | 1185 | 1 | 6.7 | 22.9 | 17.5 |
| RiceUniversity | 1 | 1 | 1 | 1395 | 1 | 6 | 18 | 2.323 |
| RochesterInst.Technology | 0 | 2 | 1 | 1185 | 0 | 6.1 | 21.8 | 17.5 |
| SeattleUniversity | 0 | 1 | 1 | 1100 | 1 | 5.3 | 19.5 | 12 |
| SetonHallUniversity | 1 | 2 | 1 | 1030 | 1 | 7.1 | 20.8 | 14.9 |
| SienaCollege | 1 | 2 | 1 | 1095 | 0 | 5.4 | 17.6 | 18.248 |
| SouthernMethodistUniversity | 1 | 2 | 1 | 1150 | 1 | 5.3 | 21.3 | 12.113 |
| St.BonaventureUniversity | 1 | 3 | 1 | 1098 | 1 | 5.1 | 17.5 | 14 |
| StanfordUniversity | 0 | 2 | 1 | 1430 | 1 | 7.3 | 27.8 | 12.774 |
| SyracuseUniversity | 1 | 1 | 1 | 1180 | 1 | 7.2 | 24.3 | 14.5 |
| TulaneUniversity | 1 | 1 | 1 | 1270 | 1 | 6.3 | 27.5 | 13.845 |
| Univ.ofChicago | 0 | 1 | 1 | 1370 | 1 | 7.3 | 28.8 | 14.073 |
| Univ.ofMiami | 1 | 2 | 1 | 1145 | 1 | 7.1 | 25.7 | 16.068 |
| Univ.ofNotreDame | 1 | 2 | 1 | 1320 | 1 | 4.8 | 23.8 | 16.572 |
| Univ.ofPennsylvania | 1 | 1 | 1 | 1355 | 1 | 7.5 | 28.6 | 17.621 |
| Univ.ofPortland | 1 | 1 | 1 | 1135 | 0 | 4.5 | 18.9 | 13.896 |
| Univ.ofScranton | 0 | 1 | 1 | 1115 | 0 | 6.6 | 21.6 | 13.5 |
| VanderbiltUniversity | 1 | 1 | 1 | 1295 | 1 | 7.1 | 27.3 | 14.5 |
| VillanovaUniversity | 1 | 2 | 1 | 1242 | 1 | 7 | 24.8 | 17.125 |
| WakeForestUniversity | 1 | 2 | 1 | 1280 | 1 | 5.2 | 23.7 | 18.703 |
| YaleUniversity | 1 | 1 | 1 | 1450 | 1 | 6.7 | 28.9 | 13.574 |
Transcribed Image Text:F-Test Two-Sample for Variances Public R&B Private R&B
F-Test Two-Sample for Variances Public Debt Private Debt
Mean
4.5500
6.3320
Mean
10.9368
14.4680
Variance
0.7784
0.9888
Variance
18.5054
14.8320
Observations
30
50
Observations
30
50
df
29
49
df
29
49
0.8036
1.1280
P(F<=f) one-tail
F Critical one-tail
0.2674
P(F<=f) one-tail
0.3477
0.5626
F Critical one-tail
1.6989
Transcribed Image Text:Type of Term
semesters - 1, quarters - 0
urban (1), suburban (2), rural (3)
private - 1, public - 0
average combined math and verbal only
1- TOEFL >= 550, 0 - otherwise
Location
Type of School
Average Total SAT
TOEFL Score
Room and Board
Recorded in thousands of dollars
Annual Total Cost
Recorded in thousands of dollars
Average Indebtedness
Recorded in thousands of dollars
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