The times in minutes to assemble a computer component for 3

The times (in minutes) to assemble a computer component for 3 different machines are listed in the table below. Workers are randomly selected.

Machine 1

Machine 2

Machine 3

32

35

28

30

29

25

31

38

29

32

33

31

34

32

29

35

36

a)   Assuming all conditions are met, test the claim that there is a difference in mean assembly time for each machine using a 5% level of significance. Use the P-value approach.

b)   What provides visual support for your decision in part (a)? Explain.

Solution

In this case we will perform one way analysis of varaiance using MINITAB to test the claim that whether there is a difference in mean assembly time for each machine using a 5% level of significance.

We wish to test the hypothesis:

H₀: there is no difference in mean assembly time for each machine i.e mean of all the 3 machines are equal

vs

H₁: there is a difference in mean assembly time for each machine i.e mean of atleast one machine is not equal to other machine mean

One-way ANOVA: M1, M2, M3

Source DF      SS     MS     F      P
Factor   2   85.45 42.72 6.95 0.008
Error   14   86.08   6.15
Total   16 171.53

Since, P-value = 0.008 < 0.05 so we will reject the null hypothesis and conclude that there is a difference in mean assembly time for each machine using a 5% level of significance.

b) From data is clear that meanof machine 2 will be greater than other two machines, whereas mean of machine 3 is smallest among the 3. This support my answer in part a)