Do the data support that public schools have a significant higher proportion of low TOEFL scores than the private schools? Show all necessary statistics and state a clear conclusion in non-statistical language. (Note: I recognize that some of the cells are small counts but we are generally ok if each cell’s expected frequency > 5). State your null and alternative hypotheses Calculate or highlight the 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 proportions of low TOEFL scores between private and public schools. 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
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
Do the data support that public schools have a significant higher proportion of low TOEFL scores than the private schools? Show all necessary statistics and state a clear conclusion in non-statistical language. (Note: I recognize that some of the cells are small counts but we are generally ok if each cell’s expected frequency > 5).
- State your null and alternative hypotheses
- Calculate or highlight the 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 proportions of low TOEFL scores between private and public schools.
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 |
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa05795a-07ea-44b9-a83e-44b537f56ea9%2F601a2f23-3d7b-4389-8858-5a35e05c4f02%2Fkrztgve_processed.png&w=3840&q=75)
![School Type
TOEFL=0 TOEFL=1
Total
Public
8
22
30
Private
7
43
50
Grand Total
15
65
80](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa05795a-07ea-44b9-a83e-44b537f56ea9%2F601a2f23-3d7b-4389-8858-5a35e05c4f02%2Fceebcln_processed.png&w=3840&q=75)
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