代写SS3843留学生、代做Java/C++语言、代做Q-Q plot、代写CS, C/C++设计

日期：2018-11-14 10:50

SS3843 Assignment 4 Questions

Due Date: Wednesday, November 14th, 2018

1) Twenty television picture tubes were randomly divided into four groups of five tubes.

The groups were coated with one of four types of coating (labelled A, B, C, D). The

conductivity of the tube was the outcome variable in the experiment. The data are given

in the table below.

Conduct Coating

56 A

55 A

62 A

59 A

60 A

64 B

61 B

50 B

55 B

56 B

45 C

46 C

45 C

39 C

43 C

42 D

39 D

45 D

43 D

41 D

a. Draw side-by-side boxplots to compare the four types of coating. Interpret the

plot.

b. Test for equality of conductivity between the four coatings.

c. Examine the assumption of normality with a Q-Q plot.

d. Test for the significance (at the 5% level) of each of the following three contrasts:

i. A versus B

ii. C verses D

iii. the average of A and B versus the average of C and D

Include all steps (e.g. hypothesis statements, test statistics, etc.).

Hint: In R, using pf(q, df1, df2, lower.tail=FALSE) where q is your

test statistic provides the p-value for an F-test.

e. Are the contrasts that were used in part (d) orthogonal? Justify your answer.

2) An experiment was run to determine whether four specific firing temperatures affect the

density of a certain type of brick. The experiment led to the following data:

Temperature Density

100 21.8 21.9 21.7 21.6 21.7

125 21.7 21.4 21.5 21.4 21.6

150 21.9 21.8 21.8 21.6 21.5

175 21.9 21.7 21.8 21.4 21.4

a. Does the firing temperature affect the density of the bricks? Use ? = 0.05.

b. Use the Least Significant Difference (LSD) method with ? = 0.05 to make

comparisons between pairs of means.

c. Use Duncan’s multiple range test with ? = 0.05 to make comparisons between

pairs of means.

d. Do you find your results from parts (b) and (c) surprising? Why or why not?

e. Analyze the residuals from this experiment. Are the analysis of variance

assumptions satisfied?

3) An article in the Journal of the Electrochemical Society (Vol. 139, No. 2, 1992, pp. 524-

532) describes an experiment to investigate the low-pressure vapour deposition of

polysilicon. The experiment was carried out in a large-capacity reactor at Sematech in

Austin, Texas. The reactor has several wafer positions, and four of these positions are

selected at random. The response variable is film thickness uniformity. Three replicates

of the experiment were run, and the data are as follows:

Wafer

Position Uniformity

1 2.76 5.67 4.49

2 1.43 1.70 2.19

3 2.34 1.97 1.47

4 0.94 1.36 1.65

a. Explain why this is a random effects experiment.

b. Estimate the variability due to wafer positions,

2.

c. Estimate the variability due to random error, 2.

d. Are there differences in the wafer positions Use = 0.05 and the one-way

ANOVA approach.

e. Analyze the residuals from this experiment. Do you think that the analysis of

variance assumptions are satisfied?

f. Are there differences in the wafer positions Use = 0.05 and the LRT approach

to determine this. How does your answer compare to part (d)?

4) An aluminum master alloy manufacturer produces grain refiners in ingot form. The

company produces the product in four furnaces. Each furnace is known to have its own

unique operating characteristics, so any experiment run in the foundry that involves more

than one furnace will consider furnaces as a nuisance. The process engineers suspect that

stirring rate impacts the grain size of the product. Each furnace can be run at four

different stirring rates. The experiment is run for a particular refiner and the resulting

grain size data is shown below.

Stirring Rate

(rpm)

Furnace

1 2 3 4

5 8 4 5 6

10 14 5 6 9

15 14 6 9 2

20 17 9 3 6

a. What type of experimental design should be used?

b. Is there any evidence that stirring rate impacts grain size Use = 0.05.

c. Graph the residuals from this experiment using a Q-Q plot. Interpret this plot.