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. Dont 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

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 LuckImportant: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)SampleMethod AMethod B11.21.421.31.731.51.541.41.351.72.061.82.171.41.781.31.6a.
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 generatorsF=BCD G=ABD
H=ABCE F=ABCD G=ACDE
H=ABDEa. 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)RunConditionY1ab12b63ad24abcd75bcd86d87ac128c10a. 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. Dont 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 LiquorTreatment1234A89889794B84779279C81878785D87928984E79818080a.
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)ABCDEFGMolaritySolute typepHGas TypeWater DepthHorn depthFlask ClampingABCDE=BCDF=ACDG=ABCy-1-1-1-1-1-1-170.61-1-1-1-11156.1-11-1-11-1149.111-1-111-158.9-1-11-111165.11-11-11-1-1323.8-111-1-11-156.8111-1-1-1169.6-1-1-1111-1100.31-1-111-1173.1-11-11-11158.411-11-1-1-178.1-1-111-1-1168.11-111-11-1312.2-11111-1-167.6111111151.9a. 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 factorsi) 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