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statistics Provide the formulas for everything the 1st time before

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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

  

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