Question

The following data represent the number of units of production per day turned out by 5 different workmen using different types of machines.
Workmen Machine type
A B C D
1 44 38 47 36
2 46 40 52 43
3 34 36 44 32
4 43 38 46 33
5 38 42 49 39

i) Test whether the mean productivity is the same for the four different machine types.
ii) Test whether 5 men differ with respect to mean productivity.

Answer 1

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Task. The following data represent the number of units of production per day turned out by 5 different workmen using different types of machines.

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

ii) Test whether 5 men differ with respect to mean productivity.

Solution. Define productivity as the number of units of production per day turned out by workman using a certain type of machines.

The mean productivity for the machine type A is $x_{A} = \frac{44 + 46 + 34 + 43 + 38}{5} = 41$ .

The mean productivity for the machine type B is $x_{B} = \frac{38 + 40 + 36 + 38 + 42}{5} = 38.8$ .

The mean productivity for the machine type C is $x_{C} = \frac{47 + 52 + 44 + 46 + 49}{5} = 47.6$ .

The mean productivity for the machine type D is $x_{D} = \frac{36 + 43 + 32 + 33 + 39}{5} = 36.6$ .

The mean productivity is not the same for the four different machine types.

The mean productivity of Workman 1 is $y_{1} = \frac{44 + 38 + 47 + 36}{4} = 41.25$ .

The mean productivity of Workman 2 is $y_{2} = \frac{46 + 40 + 52 + 43}{4} = 45.25$ .

The mean productivity of Workman 3 is $y_{3} = \frac{34 + 36 + 44 + 32}{4} = 36.5$ .

The mean productivity of Workman 4 is $y_{4} = \frac{43 + 38 + 46 + 33}{4} = 40$ .

The mean productivity of Workman 5 is $y_5 = \frac{38 + 42 + 49 + 39}{4} = 42$.

The general mean productivity $z = \frac{1}{20} (44 + 38 + 47 + 36 + 46 + 40 + 52 + 43 + 34 + 36 + 44 + 32 + 43 + 38 + 46 + 33 + 38 + 42 + 49 + 39) = 41$

All men differ with respect to mean productivity, the closest mean productivity to the general mean productivity has Workman 1.

**Answer:**

i) the mean productivity is not the same for the four different machine types;

ii) All men differ with respect to mean productivity