Homework 1 (IE 365)
Released 15 OCT 18: Due 21 Oct 18
Enclosed in the rst homework that covers your knowledge of
design of experiments. The homework is an assessment of your
prior knowledge of the topic and will be graded solely on your
eort. The main objective of this test is to establish a baseline to
gauge the level to teach material over the next two weeks.
Prior to the turn-in day/time upload all les in either a pdf or
Word document to Canvas. I will not accept pictures, but scanned
les of handwritten work is ne. I recommend that you use a
statistical or computational suite such as R, Minitab, or MATLAB,
but do what you Turn in time is local (Mountain Standard Time).
1. (Overall Concepts) (2 points) In sucient detail, describe the
dierence between independent and dependent variables in design
of experiments. Give an example and describe the dependent and
2. (Design with One Variation Source) (4 points) The data
the table below show measurements of hemoglobin (grams per
100mL) in the blood of trout. The trout were placed at random in
four dierent tanks that were given food at four levels of
sulfamerazine (0,5,10,and 15 grams of drug per 100 pounds of sh).
At 30 days, ten randomly selected sh were tested from each
trough for blood hemoglobin,.
Sulfa Concentration Hemoglobin (grams per 100mL)
0 grans 6.7 7.8 5.5 8.4 7.0 7.8 8.6 7.4 5.8 7.0
5 grams 9.9 8.4 10.4 9.3 10.7 11.9 7.1 6.4 8.6 10.6
10 grams 10.4 8.1 10.6 8.7 10.7 9.1 8.8 7.8 8.0 8.1
15 grams 9.3 9.3 7.2 7.8 9.3 10.2 8.7 8.6 9.3 7.2
(a) Plot and comment on the data.
(b) Test the hypothesis that sulfamerazine has or has no eect on
hemoglobin levels at an = 0.05.
(c) Compare the four treatments using pairwise comparisons at a
0.05 condence level. What are you conclude about what levels
cause the highest hemoglobin levels?
3. (Modeling) (2 points) Given the data from the trout
experiment, t a quadratic regression model on the data and test
the model for lack of t.
4. (Fractional Design)(2 Points): Describe why fractional design
experiments are needed. With unlimited funding and resources,
would you consider fractional design?