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?
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.
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?