3. The coating experiment, described in Excercise 7 of Chapter 7, was to study the effect of different

spray parameters on thermal spray coating properties. In the experiment, the authors attempted to

produce high-quality alumina (Al2O3) coatings by controlling the fuel ratio (factor A at 1:2.8 and

1:2.0), carrier gas flow rate (factor B at 1.33 and 3.21 L s-¹), frequency of detonations (factor C

at 2 and 4 Hz), and spray distance (factor D at 180 and 220 mm). To quantify the quality of

the coating, the researchers measured multiple response variables. In this example we will examine

the porosity (vol. %). The data are shown in the table below and can be downloaded from http:

//deanvossdraguljic.ietsandbox.net/DeanVossDraguljic/SAS-data.html.

A

B

с

D

Yijkl

A

B

C

D

2

2

2

2

5.95

2

2

2

1

2

2

1

2

1

4.57 4.03 2.17

1

2

2

2

1

2

2

2

2

1

1

1

2

1

2

1

1

1

1

1

2

1

1

1

1

2

2

1

2

1

2

1

2

Yijkl 12.28 9.57 6.73 6.07 8.49 4.92 6.95 5.31

1

2

2

3.43

2

1

2

1

1.02

2

1

1

2

4.25

2

1

1

1

2.13

1

1

1

1

(a). [3pts]. Run a model with ALL main-effects and two-way interaction effects. Write down the SAS code

copy the ANOVA table from SAS.

and

(b).[2pts] The 95% confidence interval for the difference between the two main effects of B is (

(c).[2pts] Do you believe there are significant interaction effects between B and C? Answer yes or no.

(d).[3pts] Generate an interaction plot for the B*C interaction. State how the plot supports your answer in

c. [Hint: use 1smeans B*C to get the least squares estimates, then plot it using any software of your choice.]

(e).[3pts] The 90% confidence upper limit for the error variance o² is

Show your work.