STAT 496, Spring 2003
Homework Assignment #2
1. The three fundamental principles of a designed experiment are: control of outside variables,
randomization, and replication. Consider each of the following scenarios. Does each adhere
to all three principles? If so, describe how. If not, indicate how you would change the design
to incorporate the missing principle(s). Be specific.
(a) An experiment is run to compare how different laboratories measure the breaking strength
of a special metal template. There are 6 laboratories in the experiment. Each laboratory is given a single template (like the one pictured below) and asked to measure the
strength at each of the three marked points. The six templates are all manufactured to
the same specifications. Which laboratory gets which template is randomly determined.
(b) A chemist wants to compare a new, and simpler, assay method with a standard method.
She prepares a batch of solution, divides it into 40 specimens and then selects 20 specimens at random. She asks her technician to analyze these 20 specimens using the
standard method. The chemist analyzes the other 20 specimens using the new method.
In the end, the two sets of assay results will be compared.
(c) An experiment is to be performed on the effect of drill speed on the size of drilled
holes. A single 0.25 inch drill bit in a vertical head milling machine will be used for
the experiment. All drilling will be done by the same operator. A single bar of 6061
Aluminum will be used. Four speeds will be investigated: 100, 150, 200 and 250 rpms.
The operator will pick a speed at random from the four and will drill 20 holes. The
process will be repeated, picking a speed at random from those remaining and drilling
20 holes until all 4 speeds have been used. Each of the holes will be measured using a
special caliper. The order of measurement will be random.
2. James Warren, MLCG - Flint, provided some data on two methods for measuring the tensile
strength of steel. Below are data on tensile strength for 15 test coupons using one measurement method and another 15 test coupons using a second measurement method. We are
interested in the accuracy and precision of the measurement method.
290.8
291.9
291.3
Method
294.4 293.3
293.7 295.7
294.6 295.4
1
293.4
294.6
294.7
294.8
292.5
295.7
1
293.1
297.8
299.9
Method
296.6 293.9
296.5 296.9
296.1 293.8
2
293.6
296.5
296.1
295.4
296.1
293.1
(a) Construct a dot plot of these data. Use one symbol for Method 1 and a different symbol
for Method 2.
(b) Construct a stem plot for these data. You can use a central stem with Method 1 data
coming off to the left and Method 2 data coming off to the right.
(c) Calculate a five number summary and a box plot for the data from each method.
You can put both box plots on the same page for easy comparison.
(d) Compare the Method 1 data to the Method 2 data. Compare the center, spread and
shape of the two data distributions. If you were to choose one method, which would you
choose? Why?
(e) What additional information would you like to have in order to feel more comfortable
with your choice in (d)?
3. Use the data on moisture absorption of concrete aggregates given in the analysis of variance
handout, and reproduced below. Refer to the output from the Oneway analysis from JMP
that accompanies this homework.
Example: The data below are from an experiment which studied how absorption of moisture
in concrete is affected by different aggregates. Five different concrete aggregates were studied
by exposing six samples of each to moisture for 2 days. The response variable is percent
moisture absorbed.
Yi
s2i
si
1
563
631
524
613
656
679
2
417
449
517
438
415
554
Aggregate
3
639
615
511
570
648
677
611
3,385.2
58.2
465
3,282.8
57.3
610
3,640.0
60.3
4
595
580
478
583
631
517
5
551
457
450
601
493
532
564
3,134.4
56.0
514
3,409.6
58.4
(a) From the plot of the data, do there appear to be differences between the concrete aggregates in terms of moisture absorption? If so, where do the differences appear to
be.
(b) Calculate the value for the Least Significant Difference (LSD) using t=2. Indicate which
pairs of concrete aggregates are significantly different. How does this compare to JMP
using Comparisons - Each pair, Student’s t and an individual error rate of α = 0.05?
(c) Repeat part (b) with t=3.
(d) If moisture absorption is desirable, is there a single concrete aggregate you would recommend? Why?
(e) If moisture absorption is not desirable, is there a single concrete aggregate you would
recommend? Why?
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