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In: Statistics and Probability

Question 20 Like many high school seniors, Anne has several universities to consider when making her...

Question 20

  1. Like many high school seniors, Anne has several universities to consider when making her final college choice. To assist in her decision, she has decided to use AHP to develop a ranking for school R, school P, and school M. The schools will be evaluated on five criteria, and Anne's pair-wise comparison matrix for the criteria is shown below.

Distance

Program

Size

Campus Climate

Cost

Distance

1

1/4

2

3

4

Program

4

1

4

5

6

Size

1/2

1/4

1

3

3

Climate

1/3

1/5

1/3

1

2

Cost

1/4

1/6

1/3

1/2

1


The universities' pair-wise comparisons on the criteria are shown below

  1. Distance

    R

    P

    M

    R

    1

    2

    3

    P

    1/2

    1

    3/2

    M

    1/3

    2/3

    1

    Programs

    R

    P

    M

    R

    1

    1/2

    1

    P

    2

    1

    2

    M

    1

    1/2

    1

    Size

    R

    P

    M

    R

    1

    4

    2

    P

    1/4

    1

    1/2

    M

    1/2

    2

    1

    Climate

    R

    P

    M

    R

    1

    1

    3

    P

    1

    1

    3

    M

    1/3

    1/3

    1

    Cost

    R

    P

    M

    R

    1

    1/5

    1

    P

    5

    1

    5

    M

    1

    1/5

    1

    What is the overall priority of the three universities?

    University

    Priority

    R

    0.5714

    P

    0.1429

    M

    0.2857

    University

    Priority

    R

    0.2500

    P

    0.5000

    M

    0.2500

    University

    Priority

    R

    0.3705

    P

    0.4030

    M

    0.2265

    University

    Priority

    R

    0.5455

    P

    0.2727

    M

    0.1818

    University

    Priority

    R

    0.4286

    P

    0.4286

    M

    0.1428

Solutions

Expert Solution

SOLUTION

D P S C F Normalized values Average
D 1    1/4 2    3    4    0.1644 0.1339 0.2609 0.2400 0.2500 0.2098
P 4    1    4    5    6    0.6575 0.5357 0.5217 0.4000 0.3750 0.4980
S 1/2 1/4 1    3    3    0.0822 0.1339 0.1304 0.2400 0.1875 0.1548
C 1/3 1/5 1/3 1    2    0.0548 0.1071 0.0435 0.0800 0.1250 0.0821
F 1/4 1/6 1/3 1/2 1    0.0411 0.0893 0.0435 0.0400 0.0625 0.0553
6.0833 1.8667 7.6667 12.5000 16.0000 1.0000
D
X Y Z Normalized values
X 1    2    3    0.5455 0.5455 0.5455 0.5455
Y 1/2 1    3/2 0.2727 0.2727 0.2727 0.2727
Z 1/3 2/3 1    0.1818 0.1818 0.1818 0.1818
1.8333 3.6667 5.5000 1.0000
P
X Y Z Normalized values
X 1    1/2 1    0.2500 0.2500 0.2500 0.2500
Y 2    1    2    0.5000 0.5000 0.5000 0.5000
Z 1    1/2 1    0.2500 0.2500 0.2500 0.2500
4.0000 2.0000 4.0000 1.0000
S
X Y Z Normalized values
X 1    4    2    0.5714 0.5714 0.5714 0.5714
Y 1/4 1    1/2 0.1429 0.1429 0.1429 0.1429
Z 1/2 2    1    0.2857 0.2857 0.2857 0.2857
1.7500 7.0000 3.5000 1.0000
C
X Y Z Normalized values
X 1    1    3    0.4286 0.4286 0.4286 0.4286
Y 1    1    3    0.4286 0.4286 0.4286 0.4286
Z 1/3 1/3 1    0.1429 0.1429 0.1429 0.1429
2.3333 2.3333 7.0000 1.0000
F
X Y Z Normalized values
X 1    1/5 1    0.1429 0.1429 0.1429 0.1429
Y 5    1    5    0.7143 0.7143 0.7143 0.7143
Z 1    1/5 1    0.1429 0.1429 0.1429 0.1429
7.0000 1.4000 7.0000 1.0000
D P S C F RANK
X 0.5455 0.2500 0.5714 0.4286 0.1429 0.2098 0.3705 2
Y 0.2727 0.5000 0.1429 0.4286 0.7143 0.4980 0.4030 1
Z 0.1818 0.2500 0.2857 0.1429 0.1429 0.1548 0.2265 3
1.0000 1.0000 1.0000 1.0000 1.0000 0.0821 1.0000
0.0553
1.0000

Based on the ranks, University Y is preferred.

Computations

orchestra answered 1 year ago
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