In a single factor experiment, 5 treatments are replicated 3 times each. It was found that SST = 10000 and SSTreatments = 9000. What is the value of the estimated model variance ˆσ2?
1. In a single factor experiment, 5 treatments are replicated 3 times each. It was found that SST = 10000 and SSTreatments = 9000. What is the value of the estimated model variance ˆσ2?
a) 100
b) 250
c) 500
d) 1000
e) 5000
2. In a single factor experiment, with 4 levels of the factor and 4 replications, the P-value for the Fisher LSD test on the difference of µ1 and µ2 was found to be equal to 0.04. Which of the following is a possible P-value for the same pairwise comparison using the Tukey’s test? Hint: recall that the Tukey’s test is stricter and thus would interprent any data as a weaker evidence.
a) 0
b) 0.03
c) 0.04
d) 0.05
e) 1
3. Which of the following is a contract orthogonal to Γ1 = µ1 + µ2 − µ3 − µ4?
a) Γ2 = µ1 + µ2
b) Γ2 = µ1 − µ2
c) Γ2 = µ1 − µ3
d) Γ2 = µ1 − µ4
e) Γ2 = µ1 + µ2 − 2µ3
4. An engineer wants to design an single factor experiment with 4 levels so that, if any difference D between any two means is at least 10.0, it would be able to detect that with probability of at least 0.90. Her starting guess is that 4 replications would be enough for that. What is the corresponding value of the difference parameter Φ2 assuming the model variance σ2 is equal to 25.0?
a) 1.0
b) 1.5
c) 2.0
d) 3.0
e) 5.0
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