Stat 407
Quiz 3 (Fall 2001)
Name SOLUTION
1. For the following data:
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
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



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T reat X1 X2
1
7 10 
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
1
9 11 
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2
6
5 
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2
2
4 
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2
3
5 
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3
8
6 
3
9
5
(a) (1pt) Calculate the overall mean of the sample.
X̄ =
"
6.3
6.6
#
(b) (1pt) Calculate the group means of the sample.
X̄1 =
"
8.0
10.5
#
, X̄2 =
"
3.7
4.7
#
, X̄3 =
"
8.5
5.5
#
(c) (1pt) Break up the first observation into its mean, treatment and residual component.
(7 10) = (6.3 6.6) + (8.0 − 6.3 10.5 − 6.6) + (1.0 0.5)
(d) (2pts) Given the between sums of squares (B) and within sums of squares (W) matrices below calculate the Wilks’ Λ∗ = |W|/|W + B|. Do you think this value would be significant?
B=
"
36.3 23.7
23.7 44.0
#
, W=
"
11.2 2.17
2.17 1.67
and |W| = 14.0, |W + B| = 1500.
Λ∗ = 0.0093, is likely to be significant.
2. (1pt) For the following data draw the profile plot of the first variable.
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

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T reat X1 X2
Bef ore 7 10 
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Bef ore 9 11 
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Bef ore 6
5 
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Bef ore 10 8 
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Af ter
3
5 
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Af ter
2
6 
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Af ter
5
5 
Af ter
6
8
1
#
3. The following plots correspond to the measurements from the experiments on an electronic nose. Samples
of Pepsi twist have been split in two and the noses have been set to sniff for the presence of lemon (Var 1)
and cola (Var 2). The two groups correspond to replications. The T 2 statistic for the differences between
the replications was calculated to be 17.1.
(a) (1pt) What hypothesis is the T 2 statistic testing?
Ho : δ = 0 vs Ha : δ 6= 0
(b) (1pt) If the critical value at the 5% significance level is 7.5, would you accept or reject the null
hypothesis?
Reject because the statistic is larger than the critical value.
(c) (2pts) The following plot show the data. Does the T 2 statistic match this data? (That is, could there
have been a mistake in the calculation?) Explain your answer.
No, there could not have been a mistake. There is very little difference between the two replications,
but they are all in the same trend which would result in a significant test statistic.
2