# statistics Provide the formulas for everything the 1st time before

January 30, 2017

Question
Important:

1. Provide the formulas for everything the 1st time before giving the answer. Include your SAS programs for all problems.

3. Work on your own, you are not allowed to ask a classmate about the test. If I notice copying or cheating, both get an F in the class, I do not care who copied and who provided.

4. You can only use the textbook, SAS, Excel and your notes.

1. Two different methods were used to determine the yield of a chemical. The experiment was run using eight different batches. (10 points)

Sample

Method A

Method B

1

1.2

1.4

2

1.3

1.7

3

1.5

1.5

4

1.4

1.3

5

1.7

2.0

6

1.8

2.1

7

1.4

1.7

8

1.3

1.6

a. Analyze the data as a paired data experiment using a t-test using a two sided alternative.

b. Analyze the data using randomized block design.

2. Consider the following two designs for a 28-3 fractional factorial design. (13 points)

Design I Design generators Design II Design generators

F=BCD G=ABD H=ABCE F=ABCD G=ACDE H=ABDE

a. What is the defining relation for each design.

b. What is the resolution of each design. Explain why.

c. Find the Abberation Vector for each design and explain which one (if any) is a better (Minimum Abberation) design and why.

d. How many estimable blocks will be in the alias structure.

3. Consider the following experiment: (12 points)

Run

Condition

Y

1

ab

1

2

b

6

3

2

4

abcd

7

5

bcd

8

6

d

8

7

ac

12

8

c

10

a. Write down the design matrix.

b. What is (are) the design generator(s).

c. What resolution is this design and is this the best design under this situation.

d. List all unestimable factors and the alias structure.

e. Sketch the half-normal plot using any method. Don’t comment on it. Give the graph and the table used to produce that graph.

4. A process for the manufacture of penicillin was studied. There were five variants of the basic process being studied, denoted by A, B, C, D and E. It was known that an important raw material, corn liquor, was quite variable. So each treatment was used with each different blend of corn steep liquor. (remember the interaction) (12 points)

Blend of Corn Liquor

Treatment

1

2

3

4

A

89

88

97

94

B

84

77

92

79

C

81

87

87

85

D

87

92

89

84

E

79

81

80

80

a. Analyze the data and do any plots you think are useful to test the adequacy of the model.

b. Find the 99% confidence interval for the difference between treatments A and C. Be sure to clearly state your conclusions (need lsmeans/pdiff=… cl).

c. Explain how the degrees of freedom of the error is calculated.

5. The following factors were studied to see their effect onlight intensity (y): (19 points)

A

B

C

D

E

F

G

Molarity

Solute type

pH

Gas Type

Water Depth

Horn depth

A

B

C

D

E=BCD

F=ACD

G=ABC

y

-1

-1

-1

-1

-1

-1

-1

70.6

1

-1

-1

-1

-1

1

1

56.1

-1

1

-1

-1

1

-1

1

49.1

1

1

-1

-1

1

1

-1

58.9

-1

-1

1

-1

1

1

1

65.1

1

-1

1

-1

1

-1

-1

323.8

-1

1

1

-1

-1

1

-1

56.8

1

1

1

-1

-1

-1

1

69.6

-1

-1

-1

1

1

1

-1

100.3

1

-1

-1

1

1

-1

1

73.1

-1

1

-1

1

-1

1

1

58.4

1

1

-1

1

-1

-1

-1

78.1

-1

-1

1

1

-1

-1

1

68.1

1

-1

1

1

-1

1

-1

312.2

-1

1

1

1

1

-1

-1

67.6

1

1

1

1

1

1

1

51.9

a. What kind of model is the above model? What factors are un-estimable?

What is the resolution and why?

b. Using Half-Normal Plots, Determine the active factors that affect the light intensity.

c. Using SAS and the active factors, analyze the data, remove any in-active factors. Run the

model again (Need the F-Valuses and p-values and effect estimate).

d. Test the adequacy of the final model in c. Normality plot for residuals and Predicted Vs

residuals, model fit and R2.

e. Use Tukey to determine what settings for the seven factors yield the highest light intensity.

Include the SAS output.

6. Each part of this problem is a separate problem.

a. Using ADX in SAS write down the runs for an experiment with 19 main factors and 20 runs.

i) What kind of design is this. ii) Is there an Alias structure and why.

b. If we have 16 runs with 15 main factors .

i) What kind of design is this. ii) Is there an Alias structure, if so explain it in words.

c. If you have 16 runs and 16 main factors

i) What kind of design is this. ii) Explain in two line one way to proceed with the analysis in

such a design.

(9 points)

Good Luck

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