In: Statistics and Probability
The Salem Board of Education wants to evaluate the efficiency of the town’s four elementary schools. The three outputs of the schools are
■   output 1 = average reading score
■   output 2 = average mathematics score
■ output 3 = average self-esteem score
The three inputs to the schools are
■   input 1 = average educational level of
mothers
(defined by highest grade completed: 12 = high
school graduate; 16 = college graduate, and so on)
■ input 2 = number of parent visits to school (per child)
■   input 3 = teacher-to-student ratio
The relevant information for the four schools is given in the file
P04_42.xlsx. Determine which (if any) schools are inefficient.
| Inputs | |||
| School | Input 1 | Input 2 | Input 3 | 
| 1 | 13 | 4 | 0.05 | 
| 2 | 14 | 5 | 0.05 | 
| 3 | 11 | 6 | 0.06 | 
| 4 | 15 | 8 | 0.08 | 
| Outputs | |||
| School | Output 1 | Output 2 | Output 3 | 
| 1 | 9 | 7 | 6 | 
| 2 | 10 | 8 | 7 | 
| 3 | 11 | 7 | 8 | 
| 4 | 9 | 9 | 9 | 
| Input 1 | Input 2 | Input 3 | |
| Unit costs of inputs | |||
| Output 1 | Output 2 | Output 3 | |
| Unit value of outputs | |||
| Costs/prices of inputs/outputs used | |||
| School | Input costs | Output values | |
| 1 | |||
| 2 | |||
| 3 | |||
| 4 | |||
| Selected school input cost | |||
| Selected school output value | |||
| School | Efficient or not? | ||
| 1 | |||
| 2 | |||
| 3 | |||
| 4 | |||
| Selected DEA school |