The black redstart is a bird species that migrates a relatively short distance from Germany to the Mediterranean region of Europe, whereas the common redstart travels as much as 5000 km from Germany to central Africa.  The scale in the figure below shows the duration of migratory restlessness in captive black redstarts, common redstarts, and hybrids between the two species all of which had been hand-raised under identical conditions.  (a) Why do black redstarts exhibit migratory restlessness at night for fewer days than common redstarts?  (b) What does the behavior of the hybrids tell us about the genetic differences hypotheses for the differences in duration of migratory restlessness in the two parental species?  

A 23 factorial experiment with only one replicate (8 runs) has been run in a chemical process. The response variable is molecular weight. The engineer has used the following factors:   Factor Natural levels Coded levels (x’s) A – time 80, 100 (minutes) -1, 1 B – temperature 150, 200 (deg C) -1, 1 C – concentration 30, 60 (percent) -1, 1 After conducting the experiment, the engineer computes the quantities in the following table (using coded units):   Term Effect Estimate Sum of Squares % Contribution A X 32.00 X B 6.50 X 65.44 C 1.50 4.50 3.48 AB 0.75 1.125 3.86 AC -0.50 0.50 0.39 BC 1.50 4.50 3.48 ABC -1.00 2.00 1.55   Answer the following questions (15 – 19) about this experiment.  Each question is worth 5 points.

9. Screening experiments should use conservative spacing of the factor levels.

Consider a time series with 200 observations.  Suppose that

2. When using a 2-level factorial design and the block size is not a power of 2, an optimal design can be used to construct an appropriate design.

The variance of the observations from the Hanning filter, if it is applied to a time series consisting of independent observations with constant variance σ2, is

Folding over a resolution III design is a technique to separate main effects from their two-factor interaction aliases. 

You are performing an experiment with a deterministic computer model. A reasonable choice of experimental design is 

Construct a 95% confidence interval for the regression coefficient for X1. The UCL is _______________.  

The advantage of the REML method is that it provides the standard errors of the variance components so that confidence intervals can be easily obtained.