Critical Values for Correlation Coefficient n 3 0.997 4 0.950 5 0.878 6 0.811 7 0.754 8 0.707 90.668 10 0.632 11 0.602 12 0.576 13 0.553 14 0.532 15 0.514 16 0.497 17 0.482 18 0.468 19 0.456 20 0.444 21 0.433 22 0.423 23 0.413 24 0.404 25 0.396 26 0.388 27 0.381 28 0.374 29 0.367 30 0.361 n School Name University of Rhode Island (In State) Northeastern State University(In State) Montana Tech of the University of Montana(Out of State) San Francisco State University (Out of State) University of North Texas(In State) SUNY Polytechnic Institute (In State) University of Minnesota Duluth(In State) Mount Carmel College of Nursing (Private) Cleveland State University (In State) Rutgers University New Brunswick(In State) Nebraska Methodist College of Nursing and Allied Health (Private) Baptist Memorial College of Health Sciences (Private) University of New Orleans (In State) Illinois Institute of Technology(Private) West Texas A and M University (In State) Morgan State University(In State) West Virginia University Institute of Technology(In State) Purdue University Calumet Campus(In State) Brigham Young University Provo(Private) Michigan Technological University (Out of State) Farmingdale State College(Out of State) Brigham Young University Idaho(Private) CUNY Queens College(In State) University of Mississippi(In State) Shippensburg University of Pennsylvania(In State) University of Louisiana at Monroe(In State) North Carolina A and T State University (Out of State) North Carolina A and T State University (In State) George Mason University (Out of State) SUNY Oneonta(In State) Montana State University Northern (In State) SUNY at Binghamton(Out of State) SUNY at Binghamton(In State) North Dakota State University Main Campus(Out of State) Winston Salem State University(In State) SUNY College at Geneseo(In State) Truman State University (In State) Dakota State University(In State) University of Wisconsin River Falls(In State) Northern Kentucky University(In State) University of California Berkeley (Out of State) Tarleton State University(In State) James Madison University (Out of State) Towson University(In State) Bentley University Private) University of Oklahoma Norman Campus(In State) Rutgers University Newark(In State) Graduation Rate 63 27 46 West Texas A and M University (Out of State) Stevens Institute of Technology (Private) Montana State University(In State) 53 52 44 59 73 41 59 72 36 71 44 32 21 32 83 67 49 60 60 56 43 43 43 70 72 83 55 47 81 72 39 38 89 66 44 83 53 Total 4 Year Cost 111,000 62,200 129,000 143,000 86,400 93,900 94,700 94,500 103,000 121,000 111,000 88,700 85,700 238,000 80,000 93,500 74,700 86,500 71,100 172,000 131,000 48,200 107,000 92,100 102,000 75,500 119,000 70,000 187,000 90,000 65,000 146,000 95,600 125,000 72,400 92,000 81,500 76,600 73,600 82,900 238,000 74,400 156,000 96,900 240,000 99,900 122,000 83,500 250,000 79,800 TERSSDRER-SORGTENSB-ERXDODONG-336-EFSANOORSRSRIS-R- Annual
Critical Values for Correlation Coefficient n 3 0.997 4 0.950 5 0.878 6 0.811 7 0.754 8 0.707 90.668 10 0.632 11 0.602 12 0.576 13 0.553 14 0.532 15 0.514 16 0.497 17 0.482 18 0.468 19 0.456 20 0.444 21 0.433 22 0.423 23 0.413 24 0.404 25 0.396 26 0.388 27 0.381 28 0.374 29 0.367 30 0.361 n School Name University of Rhode Island (In State) Northeastern State University(In State) Montana Tech of the University of Montana(Out of State) San Francisco State University (Out of State) University of North Texas(In State) SUNY Polytechnic Institute (In State) University of Minnesota Duluth(In State) Mount Carmel College of Nursing (Private) Cleveland State University (In State) Rutgers University New Brunswick(In State) Nebraska Methodist College of Nursing and Allied Health (Private) Baptist Memorial College of Health Sciences (Private) University of New Orleans (In State) Illinois Institute of Technology(Private) West Texas A and M University (In State) Morgan State University(In State) West Virginia University Institute of Technology(In State) Purdue University Calumet Campus(In State) Brigham Young University Provo(Private) Michigan Technological University (Out of State) Farmingdale State College(Out of State) Brigham Young University Idaho(Private) CUNY Queens College(In State) University of Mississippi(In State) Shippensburg University of Pennsylvania(In State) University of Louisiana at Monroe(In State) North Carolina A and T State University (Out of State) North Carolina A and T State University (In State) George Mason University (Out of State) SUNY Oneonta(In State) Montana State University Northern (In State) SUNY at Binghamton(Out of State) SUNY at Binghamton(In State) North Dakota State University Main Campus(Out of State) Winston Salem State University(In State) SUNY College at Geneseo(In State) Truman State University (In State) Dakota State University(In State) University of Wisconsin River Falls(In State) Northern Kentucky University(In State) University of California Berkeley (Out of State) Tarleton State University(In State) James Madison University (Out of State) Towson University(In State) Bentley University Private) University of Oklahoma Norman Campus(In State) Rutgers University Newark(In State) Graduation Rate 63 27 46 West Texas A and M University (Out of State) Stevens Institute of Technology (Private) Montana State University(In State) 53 52 44 59 73 41 59 72 36 71 44 32 21 32 83 67 49 60 60 56 43 43 43 70 72 83 55 47 81 72 39 38 89 66 44 83 53 Total 4 Year Cost 111,000 62,200 129,000 143,000 86,400 93,900 94,700 94,500 103,000 121,000 111,000 88,700 85,700 238,000 80,000 93,500 74,700 86,500 71,100 172,000 131,000 48,200 107,000 92,100 102,000 75,500 119,000 70,000 187,000 90,000 65,000 146,000 95,600 125,000 72,400 92,000 81,500 76,600 73,600 82,900 238,000 74,400 156,000 96,900 240,000 99,900 122,000 83,500 250,000 79,800 TERSSDRER-SORGTENSB-ERXDODONG-336-EFSANOORSRSRIS-R- Annual
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Critical Values for Correlation Coefficient
3 0.997
4 0.950
5 0.878
6 0.811
7 0.754
8 0.707
9 0.686
10 0.632
11 0.602
12 0.576
13 0.553
14 0.532
15 0.514
16 0.497
17 0.482
18
0.468
19 0.456
20 0.444
21 0.433
22 0.423
23 0.413
24 0.404
25 0.396
26 0.388
27 0.381
28 0.374
29 0.387
30 0.361
n
School Name
University of Rhode Island(In State)
Northeastern State University(In State)
Montana Tech of the University of Montana(Out of State)
San Francisco State University (Out of State)
University of North Texas(In State)
SUNY Polytechnic Institute (In State)
University of Minnesota Duluth(In State)
Mount Carmel College of Nursing (Private)
Cleveland State University (In State)
Rutgers University New Brunswick(In State)
Nebraska Methodist College of Nursing and Allied Health(Private)
Baptist Memorial College of Health Sciences (Private)
University of New Orleans(In State)
Illinois Institute of Technology(Private)
West Texas A and M University(In State)
Morgan State University (In State)
West Virginia University Institute of Technology(In State)
Purdue University Calumet Campus(In State)
Brigham Young University Provo(Private)
Michigan Technological University (Out of State)
Farmingdale State College(Out of State)
Brigham Young University Idaho(Private)
CUNY Queens
College(In State)
University of Mississippi(In State)
Shippensburg University of Pennsylvania(In State)
University of Louisiana at Monroe(In State)
North Carolina A and T State University (Out of State)
North Carolina A and T State University(In State)
George Mason University(Out of State)
SUNY Oneonta(In State)
Montana State University Northern(In State)
SUNY at Binghamton(Out of State)
SUNY at Binghamton(In State)
North Dakota State University Main Campus (Out of State)
Winston Salem State University(In State)
SUNY College at Geneseo(In State)
Truman State University(In State)
Dakota State University(In State)
University of Wisconsin River Falls(In State)
Northern Kentucky University(In State)
University of California Berkeley(Out of State)
Tarleton State University (In State)
James Madison University (Out of State)
Towson University(In State)
Graduation
Rate
63
Bentley University(Private)
University of Oklahoma Norman Campus (In State)
Rutgers University Newark(In State)
West Texas A and M University (Out of State)
Stevens Institute of Technology(Private)
Montana State University(In State)
JERSSAN
41
88388:
80
59
72
36
71
44
32
21
32
83
87
49
56
60
60
56
43
43
43
70
72
26
88888888828958888
83
81
72
39
54
38
43
71
68
44
83
53
Total 4
Year Cost
111,000
62,200
129,000
143,000
86,400
93,900
94,700
94,500
103,000
121.000
111,000
88,700
85,700
238,000
80,000
93,500
74,700
86,500
71,100
172,000
131,000
48,200
107,000
92,100
102,000
75,500
119,000
70,000
187,000
90,000
65,800
146,000
95,600
125,000
72,400
92,000
81,500
76,600
73,800
82,900
238,000
74,400
156.000
96,900
240,000
99,900
122,000
83,500
250,000
79,800
Annual
ROI
7.8
6.6
8.9
6.7
7.8
8.1
7.7
9
6.5
8.9
7.5
9.1
8.1
6.4
7.2
6.8
10.7
8
11.8
7.7
7.4
12.6
8.3
6.7
6.3
8.2
6.2
9
6.4
6.5
6.7
8
10.4
7.1
6.8
7.7
7.4
8.3
6.5
7.6
6.9
7.5
6.9
7.7
6.4
8.6
8.5
7
7.6
9
Transcribed Image Text:The data represent the cost, return on investment, and graduation rate for a random sample of fifty colleges or universities in the United States. The data is from payscale.com. The variable "Cost" represents the four-year cost including tuition, supplies, room and board of attending the school. The variable "Annual ROI" represents the return on investment for graduates of the school. It essentially represents how much you would earn on the
investment of attending the school. The variable "Grad Rate" represents the graduation rate of the school. Complete parts (a) and (b) below.
Click here to view the school data.
Click here to view the table of critical values of the correlation coefficient.
(a) Describe the association between Cost and Graduation Rate graphically by drawing a scatter diagram, treating Cost as the explanatory variable. Describe the association between Cost and Graduation Rate by finding the linear correlation between the two variables. Is there a linear association between Cost and Graduation Rate? Note: Use the critical value for n=30 from the accompanying table.
Draw a scatter diagram of the data. Choose the correct diagram below.
A.
100-
Ong
30,000 260,000
Determine the linear correlation coefficient between Cost and Graduation Rate.
r= (Round to three decimal places as needed.)
Cost
Because the correlation coefficient is
(Round to three decimal places as needed.)
10
6
30,000
260,000
Q
Q
and the absolute value of the correlation coefficient is
Determine the linear correlation coefficient between Cost and Annual ROI.
r= (Round to three decimal places as needed.)
Because the correlation coefficient is
(Round to three decimal places as needed.)
OB.
and the absolute value of the correlation coefficient is
E
100-
Og
30,000 260,000
OB.
than the critical value for this data set. (use n = 30).
Cost
10
30,000
Q
Q
Cost
(b) Describe the association between Cost and Annual ROI graphically by drawing a scatter diagram, treating Cost as the explanatory variable. Describe the association between Cost and Annual ROI by finding the linear correlation between the two variables. Is there a linear association between Cost and Annual ROI? Note: Use the critical value for n = 30 from the accompanying table.
Draw a scatter diagram of the data. Choose the correct diagram below.
OA
260,000
G
Q
than the critical value for this data set. (use n=30)
OC.
100-
0
30,000
linear relation exists between the two variables.
OC.
67
30,000
260,000
linear relation exists between the two variables.
Cost
meng
260,000
Q
Q
Cost
O D.
100-
30,000 260,000
Ong)
Cost
OD
10-
30,000
Cost
260,000
Expert Solution
Step 1
Solution:
The data for the Graduation rate, Cost and Annual ROI is given.
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