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Math1302: Design and Analysis of Experiments Submit by the Due Date

Assignment 2 (100 points worth 10%) Due date: As shown on canvas

Student number: Student name:

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INSTRUCTIONS

Please work through all problems using a statistical package where and if required. You will need to create a Word document to copy your codes, outputs and comments into and prepare your written answers to the questions below, otherwise you might use RMarkdown and submitted as pdf file.

Submit online through Canvas by the due day.

Question 1: The ANOVA table from a randomized complete block experiment is shown below.

20 169.33 29 1503.71

a) Fill in the blanks (shown as ?). You may give bounds on the P-value and not the exact answer.

b) How many blocks were used in this experiment?

c) What conclusions can you draw?

(15 points)

Question 2: Considerthesinglefactorcompletelyrandomizedsinglefactorexperimentshownbelow.Supposethat this experiment had been conducted in a randomized complete block design, and that the sum of squares for blocks was 80.00. Modify the ANOVA for this experiment to show the correct analysis for the randomized complete block experiment.

25 186.53 29 1174.24

(10 points)

Question 3: An experiment was run to determine whether four specific fire temperatures affect the density of a certain type of brick. A completely randomized experiment led to the following data:

Treatment Block Error Total

DF SS MS F P

Temperature

21.8 21.9 21.7 21.6 21.7

21.7 21.4 21.5 21.4

21.9 21.8 21.8 21.6 21.5

21.9 21.7 21.8 21.4

a) Does the fire temperature affect the density of the bricks? Use α = 0.05%.

Error Total

DF SS MS F P

RMIT Classification: Trusted

b) Is it appropriate to compare the means using the Fisher LSD method (for example) in this experiment?

c) Analyse the residuals from this experiment. Are the assumptions of analysis of variance satisfied?

(15 points

Question 4: Suppose you wish to determine whether there are differences in the average prices among 3 major supermarkets in Melbourne. You randomly select 8 regularly bought items, each distinct item of the same brand, and observe their unit prices at each supermarket. The following data were obtained:

Supermarket

3 4 5 6 7 8

1.10 3.75 3.80 0.77 0.75 1.59 1.54 0.82 0.77 0.65 0.68

1.08 3.70 0.77 1.63 0.77 0.59

a) Is there a need to block the items? Why?

b) What other aspects could be considered that may influence the prices that are being recorded?

c) Visually represent the collected data. Are there any visible differences for the average prices for the 3

supermarkets?

d) Use the analysis of variance procedure to test the null hypothesis of no treatment effects.

e) Based on your answer on d) should you use a multiple comparison method (i.e. LSD) here? Explain.

(25 points)

Q u e s t i o n 5 : An industrial engineer is investigating the effects of four assembly methods (A, B, C, and D) on the assembly time for a colour television component. Four operators are selected for the study. Furthermore, the engineer knows that each assembly method produces such fatigue that the time required for the last assembly may be greater than the time required for the first, regardless of the method. That is, a trend develops in the required assembly time. To account for this source of variability, the engineer uses the Latin square design shown below. For the generation of the data you need the 3rd and 6th numerical digit from your student number as you denote this on the top of this assignment.

Order of Assembly

I II III IV

C=s3+5 D=14 A=7 B=8

B=7 C=18 D=11 A=8

A=5 B=10 C=11 D=9

D=10 A=10 B=12 C=s6+8

a) Test if there is a difference between the four assembly methods. State the hypotheses and use α=0.05% for the test.

b) Obtain the estimates of the treatment effects.

c) Use Tukey’s method to perform pairwise comparison.

d) Check the required assumptions for the method used in question 5a.

e) Suppose that the engineer does not know that each assembly method produces such

fatigue every time and the only information available is the recorded assembly time, the method used and the operators. Using the data as displayed above, answer the following questions:

• What is the design that is applied in this situation?

• Write the data above in the needed format based on the design you suggested. Test whether the assembly method is significant in this new design.

(35 points)

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