Page 255 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Average production by the type of machine
Quantitative Techniques-II
A B C D
Worker 1 25 26 23 28
Worker 2 23 22 24 27
Notes
Worker 3 27 30 26 32
Worker 4 29 34 27 33
The firm is interested in knowing:

(a) Whether the mean productivity of workers is significantly different.
(b) Whether there is a significant difference in the mean productivity of different types of
machines.
Illustration: Company ‘X’ wants its employees to undergo three different types of training
programme with a view to obtain improved productivity from them. After the completion of
the training programme, 16 new employees are assigned at random to three training methods
and the production performance was recorded.
The training manager’s problem is to find out if there are any differences in the effectiveness of
the training methods? The data recorded is as under:

Daily output of new employees

Method 1 15 18 19 22 11
Method 2 22 27 18 21 17
Method 3 18 24 19 16 22 15

Following steps are followed.
1. Calculate Sample mean i.e. x

2. Calculate General mean i.e. x


 n x  x  2
i
i
2
3. Calculate variance between columns using the formula  
k  1
where K = (n + n + n -3).
1 2 3
4. Calculate sample variance. It is calculated using formula:
2
2   x   x
i
Sample variance s  where n is No. of observation under each method.
i
n 1

2  n  1
5. Calculate variance within columns using the formula   i
n  k
r
 between column variance
6. Calculate F using the ratio F =  
 within column variance 
7. Calculate the number of degree of freedom in the numerator F ratio using equation, d.f =
(No. of samples -1).
8. Calculate the number of degree of freedom in the denominator of F ratio using the equation

d.f = n   k
i
9. Refer to F table f8 find value.
10. Draw conclusions.

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