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Important:

1.

Provide the formulas for everything the 1st

time before giving the answer. Include your SAS programs for all problems.

2. Approximate

your numbers to four decimals and highlight all-important answers.

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

ad

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

Flask Clamping