HOMEWORK #1 due Wednesday 2-20
NOTE: Organize your homework in the following order:
Problem 1. Seven cars (7) were chosen from each of 5 similar types of car. In randomized order, each car was driven over a test course. Fuel efficiencies are given in Table 1.
Table 1. Fuel efficiencies of cars of 5 types
------------------------------------------------
A 189 202 194 215 206 241 166
B 132 181 128 195 135 182 136
C 200 187 181 200 194 200 170
D 173 159 160 154 181 155 216
E 183 227 154 225 172 185 234
Use SAS to answer the following questions:
proc print
to make sure that you have entered the data correctly.
oneway.sas on the Math420 Web site.
Note that oneway.sas has three alternative ways to import
data from a one-way layout into a SAS dataset, one of which allows you to
enter the data exactly as in Table 1. Use whatever format seems
easiest.)
proc chart with option vbar yield /
subgroup=type.)
proc
univariate normal plot with var resid. See
oneway.sas).
Problem 2. In the text, Problem 4 page 171 considers the effects of four treatments A,B,C,D in 32 consecutive trials for a process that looks like it might be unstable over time.
Block=1 for observations
n=1,2,3,4, Block=2 for observations
n=5,6,7,8, up to Block=8 for
n=29,30,31,32. Then test the hypothesis H_0 of
part (ii) in a randomized block design with two factors, treatment
and (time) Block. Do you accept or reject H_0 in the randomized block
design? What is the P-value for Treatment? Is it less or more than in
part (ii)?
Problem 3. Consider the burn data in Problem #2, Chapter 4, on page 170 of the text.
Problem 4. An investigator wants to study the yield of a chemical process depending on a particular catalyst as a function of batch, level of acidity, settling time, and catalyst concentration. Since only 5 batches of the raw material was available, and each batch has only enough material for 5 runs, the investigator chose to use a Greco-Latin square design. She measured yield for 5 different runs for each batch with Acidity, Settling time (A,B,C,D,E), and Catalyst concentration (al,be,ga,de,ep) set as in Table 2 below. The yield results of her 25 runs are also in Table 2.
Table 2. Yields of a chemical process
Acid Concentration
Batch 1 2 3 4 5
------------------------------------------------------------
1 A,al=26 B,be=16 C,ga=19 D,de=16 E,ep=13
2 B,ga=18 C,de=21 D,ep=18 E,al=11 A,be=21
3 C,ep=20 D,al=12 E,be=16 A,ga=25 B,de=13
4 D,be=15 E,ga=15 A,de=22 B,ep=14 C,al=17
5 E,de=10 A,ep=24 B,al=17 C,be=17 D,ga=14
Use SAS to
Problem 5. Consider the data in Problem 8, p227, of the text:
Table 3. Yield as a function of three factors
Run Temp Catal pH Week1 Week2
------------------------------------
1 L L L 60.4 62.1
2 H L L 75.4 73.1
3 L H L 61.2 59.6
4 H H L 67.3 66.7
5 L L H 66.0 63.3
6 H L H 82.9 82.4
7 L H H 68.1 71.3
8 H H H 75.3 77.1
where L,H are low and high values. Answer the following questions, using
SAS if convenient:
Problem 6. Consider the data in Problem 20, p233, of the text:
Table 4. Impurities in a Chemical Process
as a Function of Four Factors
Run Conc NaOH Speed Temp Impurities
---------------------------------------------
1 L L L L 38
2 H L L L 40
3 L H L L 27
4 H H L L 30
5 L L H L 58
6 H L H L 56
7 L H H L 30
8 H H H L 32
9 L L L H 59
10 H L L H 62
11 L H L H 53
12 H H L H 50
13 L L H H 79
14 H L H H 75
15 L H H H 53
16 H H H H 54
where L,H are low and high values. Answer the following questions, using
SAS if convenient:
FourFac.sas or NormPlot.sas
on the Math420 Web site.)