Question

The table below contains observations of breakdown time of 3 different machines at a manufacturing site. The production manager believes that the main reason for machines breaking down is the difference in quality of raw material that comes from 3 different sources. On the contrary, the procurement department, which is responsible for supplies, considers as the main reason the old age of some production machines and their poor maintenance. Some young machine operators believe that the problem is more complicated; certain machines work more efficiently with certain types of raw materials and less efficiently with others. The file contains 30 observations that were collected during 3 weeks (21 days). Each machine operates with only one type of material every day. Observations record machine type, supplier of raw material and break down time (minutes) during the day.

Use the proper statistical test to check whether factors like the machine type, the kind of raw material, or a combination effect, affect the break time. Report your conclusions in context.

The table is

Obs.#	Raw Materials Supplier	Machine Type	BDT (minutes)
1	Tynisia	B	70
2	Egypt	C	80
3	Egypt	A	66
4	Egypt	C	79
5	Lebanon	A	90
6	Lebanon	A	90
7	Tynisia	A	88
8	Tynisia	C	92
9	Egypt	B	98
10	Tynisia	C	79
11	Egypt	A	61
12	Egypt	C	77
13	Egypt	C	63
14	Egypt	B	93
15	Lebanon	A	71
16	Lebanon	C	92
17	Tynisia	A	73
18	Lebanon	C	95
19	Lebanon	B	82
20	Lebanon	B	90
21	Lebanon	B	94
22	Lebanon	A	95
23	Tynisia	B	72
24	Egypt	C	78
25	Lebanon	A	95
26	Lebanon	C	90
27	Tynisia	A	87
28	Tynisia	C	77
29	Tynisia	B	65
30	Lebanon	A	87

Answer 1

The output is:

The hypothesis being tested is:

H₀: There is no effect of Machine Type on the break time

H_a: There is an effect of Machine Type on the break time

The p-value from the output is 0.699.

Since the p-value (0.699) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that there is an effect of Machine Type on the break time.

The hypothesis being tested is:

H₀: There is no effect of the kind of raw material on the break time

H_a: There is an effect of the kind of raw material on the break time

The p-value from the output is 0.011.

Since the p-value (0.011) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is an effect of the kind of raw material on the break time.

The hypothesis being tested is:

H₀: There is no interaction effect of the kind of raw material & Machine Type on the break time

H_a: There is an interaction effect of the kind of raw material & Machine Type on the break time

The p-value from the output is 0.001.

Since the p-value (0.001) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is an interaction effect of the kind of raw material & Machine Type on the break time.