Question

You are the production manager at a parachute manufacturing company. Parachutes are woven in your factory using a synthetic fiber purchased from 1 of 4 different suppliers. The factory uses 2 types of looms, the Athenian and the Spartan. You are concerned about the consistency of parachute strength, so you measure the strength for 5 parachutes made with each of the 4 fiber suppliers, using each of the 2 looms.

Perform an ANOVA with these data for main effects and interaction effects.
Use Minitab software to find the solution.

Strength	Supplier	Loom
20.6	1	Athenian
18.0	1	Athenian
19.0	1	Athenian
21.3	1	Athenian
13.2	1	Athenian
18.5	1	Spartan
24.0	1	Spartan
17.2	1	Spartan
19.9	1	Spartan
18.0	1	Spartan
22.6	2	Athenian
24.6	2	Athenian
19.6	2	Athenian
23.8	2	Athenian
27.1	2	Athenian
26.3	2	Spartan
25.3	2	Spartan
24.0	2	Spartan
21.2	2	Spartan
24.5	2	Spartan
27.7	3	Athenian
18.6	3	Athenian
20.8	3	Athenian
25.1	3	Athenian
17.7	3	Athenian
20.6	3	Spartan
25.2	3	Spartan
20.8	3	Spartan
24.7	3	Spartan
22.9	3	Spartan
21.5	4	Athenian
20.0	4	Athenian
21.1	4	Athenian
23.9	4	Athenian
16.0	4	Athenian
25.4	4	Spartan
19.9	4	Spartan
22.6	4	Spartan
17.5	4	Spartan
20.4	4	Spartan

Answer 1

We perform a two way ANOVE to test if there is a significant effect due to the factors and if there a significant interaction effect.

The two factors are "4 fiber suppliers" (levels (1,2,3,4 ) and the 2 "looms".(level Athenian and Spartan)

The steps to do two way ANOVA in minitab is as follows:

1. Open mintab and feed the data into the cells provided giving appropriate Column names.
2. From the toolbar above depending on whether you have minitab 16 or a higher version select the appropriate option:
3. Now in the options that come in the "Responses" tab select the option "Strength" from the options on the side, and in the "Factors" tab select the option "Supplier" and "Loom" from the options on the side.
4. Then click on the option "Model" from below. In the dialogue box that appears you will see the following:
5. Put two in the interactions option. Select both "Supplier" and "Loom" in the terms in the model option and lick on the add the button on the Cross factors, covariates, and terms in the model line). This will add the interaction term between the two factrs into the Terms in the model: box, as shown below:
6. Click on "OK" to return to the General linear model dialogue box and click on "OK" again to display the results.

The ANOVA table obtained should have the following values:

From the above table we see that there is a significant effect due on the strength of the parachuttes due to the "Supplier" Type however there is no significant effect on the strength of the parachuttes due to the "Loom" types and also there is no significant interaction effect between the "Supplier" and "Loom" effects.