Reference no: EM132181421
STAT Assignment -
Question 1 - Montgomery Problem
An experiment is designed to study pigment dispersion in paint. Four different mixes of a particular pigment are studied. The procedure consists of preparing a particular mix and then applying that mix to a panel by three application methods (brushing, spraying, and rolling). The response measured is the percentage reflectance of pigment. Three days are required to run the experiment, and the data obtained follow. Analyze the data and draw conclusions, assuming that mixes and application methods are fixed.
|
Day
|
Applicable Method
|
Mix
|
|
1
|
2
|
3
|
4
|
|
1
|
1
|
64.5
|
66.3
|
74.1
|
66.5
|
|
2
|
68.3
|
69.5
|
73.8
|
70.0
|
|
3
|
70.3
|
73.1
|
78.0
|
72.3
|
|
2
|
1
|
65.2
|
65.0
|
73.8
|
64.8
|
|
2
|
69.2
|
70.3
|
74.5
|
68.3
|
|
3
|
71.2
|
72.8
|
79.1
|
71.5
|
|
3
|
1
|
66.2
|
66.5
|
72.3
|
67.7
|
|
2
|
69.0
|
69.0
|
75.4
|
68.6
|
|
3
|
70.8
|
74.2
|
80.1
|
72.4
|
Question 2 - Montgomery Problem
An article in Quality Engineering ("Quality Quandries: Two-Level Factorials Run as Split-Plot Experiments," Bisgaard et al., Vol. 8, No. 4, pp. 705-708, 1996) describes a 25 factorial experiment in a plasma process focused on making paper more susceptible to ink. Four of the factors (A-D) are difficult to change from run to run, so the experimenters set up the reactor at the eight sets of conditions specified by the low and high levels of those factors, and then processed the two paper types (factor E) together. The placement of the paper specimens in the reactor (right versus left) was randomized. This produces a split-plot design with A-D as the whole-plot factors and factor E as the subplot factor. The data from this experiment are shown in Table P14.4 (attached). Analyze the data from this experiment and draw conclusions.
Question 3 -
Ten subjects agreed to be in a study to examine the concentration of a drug in the bloodstream for two different dosage forms (capsule and tablet). It is assumed that the higher the concentration the better (within limits). Subjects fasted the night prior to starting the study until 4 hours after ingestion of the drug. Blood samples were obtained immediately preceding the assigned dosage and at .5, 1, 2, 3 and 4 hours after dosing. This data set is called drugconc.d a t and has the observed times for each subject on one data line. The second column denotes tablet (1) or caplet (2). Analyze the data and present your conclusions. (Hint: An interaction plot would be helpful).
Question 4 -
A famous data set by Potthoff and Roy (1964) looks at the distance (mm) from the center of the pituitary gland to the pteryomaxillary fissure in 16 boys and 11 girls. Measurements were taken at ages 8, 10, 12, and 14 years. This distance (as it changes over time) is important in orthodonic therapy. For this problem, consider using a mixed model to describe these data. Consider the CS, AR(1), and TOEP correlation structures and present conclusions based on the best fitting correlation structure. These conclusions should address if there are sex differences, whether the distance changes over time, and whether this change is consistent across the two sexes. The data set is on the webpage.
Question 5 -
Consider the data set in Montgomery Problem given below.
a. Use Yates' algorithm to estimate the factor effects. This process can be simplified into a single run by using the sum of the three replicates as the data.
b. Use these results to also compute the SS.
c. Verify your SS results by performing ANOVA using SAS (data set on the webpage).
d. Which combination of factors results in the longest tool life?
Montgomery Problem - An engineer is interested in the effects of cutting speed (A), tool geometry (B), and cutting angle (C) on the life (in hours) of a machine tool. Two levels of each factor are chosen, and three replicates of a 23 factorial design are run. The results are as follows:
|
A
|
B
|
C
|
Treatment Combination
|
Replicate
|
|
I
|
II
|
III
|
|
-
|
-
|
-
|
(1)
|
22
|
31
|
25
|
|
+
|
-
|
-
|
a
|
32
|
43
|
29
|
|
-
|
+
|
-
|
b
|
35
|
34
|
50
|
|
+
|
+
|
-
|
ab
|
55
|
47
|
46
|
|
-
|
-
|
+
|
c
|
44
|
45
|
38
|
|
+
|
-
|
+
|
ac
|
40
|
37
|
36
|
|
-
|
+
|
+
|
bc
|
60
|
50
|
54
|
|
+
|
+
|
+
|
abc
|
39
|
41
|
47
|
Question 6 - Montgomery Problem
I am always interested in improving my golf scores. Since a typical golfer uses the putter for about 35-45 percent of his or her strokes, it seems reasonable that improving one's putting is a logical and perhaps simple way to improve a golf score ("The man who can putt is a match for any man:'-Willie Parks, 1864-1925, two time winner of the British Open). An experiment was conducted to study the effects of four factors on putting accuracy. The design factors are length of putt, type of putter, breaking putt versus straight putt, and level versus downhill putt. The response variable is distance from the ball to the center of the cup after the ball comes to rest. One golfer performs the experiment, a 24 factorial design with seven replicates was used, and all putts are made in random order. The results are shown in Table P6.4 (attached).
(a) Analyze the data from this experiment. Which factors significantly affect putting performance?
(b) Analyze the residuals from this experiment. Are there any indications of model inadequacy?
Note - All answers to be completed in SAS. All SAS input and output must pasted in to the solutions. Other Statistical software, such as Minitab, JMP, SPSS, R, and MATLAB, are also allowed to use.
Note: Question 1 and 2 are related to Nested and Split-Plot designs, Question 5 and 6 are related to factorial design. And Data file for question 3, 4, 5 and 6 are attached.
Attachment:- Assignment Files.rar