Question

The following data represent the number of units of production per day turned out by 3 different workmen using different types of machines:
Workman
Machine Types

A
44
46
34

B
38
40
36

C
47
52
44

D
36
43
32


(a) Test whether the mean productivity is the same for the four different machine types.

(b) Test whether three men differ with respect to mean productivity.​

Answer 1

Answer:

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Answer 2

Answer:

a) All machine types have different mean productivity

b) All workmen differ with respect to mean productivity

Step-by-step explanation:

Concept: $Mean = \frac{Sum of Elements}{number of Elements}$

Solution:

The mean productivity for machine type A,  $m_{A} = \frac{44+ 46+34}{3} = 41.33$

The mean productivity for machine type B,  $m_{B} = \frac{38 + 40 + 36}{3} = 38$

The mean productivity for machine type C,  $m_{C} = \frac{47 + 52 + 44}{3} = 47.66$

The mean productivity are not same for the machines.

The mean productivity of workman 1,  $w_{1} = \frac{44 + 38 + 47 + 36}{4} = 41.25$

The mean productivity of workman 2,  $w_{2} = \frac{46 + 40 + 52 + 43}{4} = 45.25$

The mean productivity of workman 3,  $w_{3} = \frac{34 + 36 + 44 + 32}{4} = 36.5$

The general mean productivity, $w = \frac{1}{12}(44 + 46 + 34 + 38 + 40 + 36 + 47 +52 + 44 + 36 + 43 + 32) = 41$

All workmen differ to mean productivity, the closest mean productivity to the general productivity is workman 1.

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