STA 6208 – Exam 3 – Spring 2012 – PRINT Name ___________________________
Conduct Individual Test/CI’s at  = 0.05 significance level, and all simultaneous tests/CI’s @ experimentwise rate 0.05
Q.1. A 23 factorial experiment is conducted to determine the main effects and interactions among 3 factors
(presence/absence) on taste quality for frozen dinners. The following table gives the design, mean, and standard
deviation (SD) for the 8 combinations of factor levels. There were 3 replicates per treatment.
Trt
(1)
a
b
c
ab
ac
bc
abc
A
-1
1
-1
-1
1
1
-1
1
B
-1
-1
1
-1
1
-1
1
1
C
-1
-1
-1
1
-1
1
1
1
AB
1
-1
-1
1
1
-1
-1
1
AC
1
-1
1
-1
-1
1
-1
1
BC
1
1
-1
-1
-1
-1
1
1
ABC
Mean
40
64
24
36
68
76
20
80
SD
3
2
2
3
1
3
2
2
p.1.a. Give the +1/-1 levels for the ABC Interaction in the table above.
p.1.b. Compute MSE
p.1.c. Compute l A 
n
k y ,
i 1
i
i
SSA 
r
2
l
n  A
2
where ki  1
Test H0: No Factor A effect
Q.2. An experimenter wishes to conduct a taste experiment to determine whether there are differences in the 6 recipes that
are to be compared. He plans to have individuals serve as blocks and taste items from the various recipes. However, he
knows that individuals have a difficult time choosing a favorite as the number of choices increases. He has selected a
sample of 10 raters, and has decided that each will choose his/her favorite among 3 recipes. Complete the following parts,
where t = # trts, b=# blocks, r = reps/trt, k = block size,  = 3 blocks each pair of treatments appear in together.
p.2.a. t = ___________ b = ___________ r = ___________ k = ___________  = ___________
p.2.b. Put a check in each appropriate cell for this design to meet the criteria in part p.2.a.
Recipe1
Recipe2
Recipe3
Recipe4
Recipe5
Recipe6
Rater1
Rater2
Rater3
Rater4
Rater5
Rater6
Rater7
Rater8
Rater9
Rater10
Q.3. A study was conducted as a Latin Square design with 5 packages (treatments), in 5 stores (Rows), over 5 weeks
(Columns). The response was number of packages sold in a week. The Error sum of squares was reported to be 600.
Compute Tukey’s HSD and Bonferroni’s MSD for comparing all pairs of package means.
Q.5. A study compared 3 foods on serum glucose levels. A sample of 12 subjects were selected, and randomized such
that 4 people received Food A, 4 received Food B, and 4 received Food C. Each subject’s glucose levels were observed at
3 time points after eating the meal (15, 30, and 45 minutes).
p.5.a. Complete the following ANOVA table.
Source
Food
Subject(Food)
Time
Food*Time
Error2
Total
df
SS
MS
F
F(.05)
Significant?
1020.67
413.33
170.17
869.67
128.17
2602.00
p.5.b. The means for each food/time combination are given below. Use Bonferroni’s method to compare all
pairs of food, separately for each time (treat each time as a separate “family”, when making adjustment).
Food\Time
1
2
3
Time 1:
Food1
1
19
22
26
2
35
20
27.25
Food2
Food3
3
31.5
11.5
35.75
Time 2:
Food2
Food3
Food1
Time 1:
Food2
Food1
Food3
Q.6. A study was conducted to compare 5 Nitrogen levels (0, 45, 90, 135, 180 kg/hectare) and Rice Straw
(Absent/Present) on Rice Grain Yield (100s of kg/hectare). The experiment was conducted as a split-plot design, with
whole plot factor being Nitrogen level, and sub-plot factor being Rice Straw. The experiment was conducted in 3 blocks
(Years).
p.6.a. Complete the following Analysis of Variance Table.
ANOVA
Source
WP
Block
WP*Block
SP
WP*SP
Error
Total
df
SS
MS
F
F(.05)
5693.63
216.82
60.18
110.82
0.96
6098.94
p.6.b. Assuming no significant Nitrogen/Rice Straw Interaction, compute Bonferroni’s Minimum significant Difference
for comparing pairs of Nitrogen level effects. Show which levels are significantly different.
Nitrogen
0
45
90
135
180
Mean
48.65
75.19
79.07
85.85
85.96
Rice Straw
0
1
Bonferoni MSD = ________________________
Mean
73.02
76.87
Nit0
Nit45
Nit90
Nit135
Nit180
p.6.c. Compute a 95% Confidence Interval for the effect of Using Rice Straw, versus not using rice straw.