Lecture 5 FieldworkRandom sampling from 4 normally distributed populations produced the following data. Input into SPSS
and using the univariate GLM perform the following steps.
Treatments
A
B
C
D
-11
-8
-8
-12
-13
-13
-13
-13
-10
-15
-8
-15
-12
-13
-10
Xbar = -11.3
Xbar = -12
Xbar = -10.4
Xbar = -13.3
Sample var = 2.33
Sample var = 8.7
Sample var = 6.3
Sample var = 2.3
a. Specify the competing hypotheses in order to determine where some differences exist between
the population means
b. Calculate the value of the F test statistic
c. Approximate the p value
d. At the 10% significance level, what is the conclusion?
One of our well known conglomerate claims that its detergent whitens and brightens better than all the
rest. In order to compare the cleansing action of the top three brands of detergents, 24 swatches of
white cloth were soiled with red wine and grass strains and then washed in front loading machines with
respective detergents. The following whiteness readings were obtained. Input into SPSS and using the
univariate GLM perform the following steps.
Detergent
1
2
3
84
78
87
79
74
80
87
81
91
85
86
77
94
86
78
89
89
79
89
69
77
83
79
78
Xbar = 86.3
Xbar = 80.3
Xbar = 80.9
Sample var = 20.8 = s^2
Sample var = 45.1
Sample var = 27.3
Grand mean = 82.5
a. Construct an ANOVA table. Assume whiteness readings are normally distributed.
b. Specify the competing hypotheses to test whether there are some differences in the average
whitening effectiveness of the three detergents.
c. At the 5% significance level, what is the conclusion to the test?
d. If there are differences, now I would like to find out specific differences between each pair of
detergents. Which pairs differ?
One of the researchers conducts a 2 way ANOVA test with interaction to see if the interaction of the
brand of the detergent and the specific market makes a significant difference to the product. He
provides the following ANOVA table.
a.
Find the missing values in the ANOVA table.
Source
SS
Df
Markets
752.78
Detergents
MS
F
p-value
F crit
2
0.0116
3.885
12012.5
1
5.62e-09
4.747
Interaction
58.33
2
0.6117
3.885
Within
683.33
12
(row)
Total
13506.94
17
b. At the 5% significance level, can you conclude that there is an interaction effect?
c. At the 5% significance level, can you conclude that the column means differ?
d. At the 5% significance level, can you conclude that the row (sample) means differ?
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