5 An engineer wishes to investigate the effects of both adhesive type and conductor
Example 1.5 An engineer wishes to investigate the effects of both adhesive type and conductor
material on bond strength when mounting an integrated circuit (IC) on a certain sub- strate. Two adhesive types and two conductor materials are under consideration. Two observations are made for each adhesive-typeconductor-material combination, resulting in the accompanying data:
Adhesive Type
Conductor Material
Observed Bond Strength Average
The resulting average bond strengths are pictured in Figure 1.3. It appears that adhe- sive type 2 improves bond strength as compared with type 1 by about the same amount whichever one of the conducting materials is used, with the 2, 2 combina- tion being best. Inferential methods can again be used to judge whether these effects are real or simply due to chance variation.
Average strength
85 Adhesive type 2
Adhesive type 1 80
1 2 Conducting material
Figure 1.3 Average bond strengths in Example 1.5
Suppose additionally that there are two cure times under consideration and also two types of IC post coating. There are then 2 ? 2 ? 2 ? 2 5 16 combinations of these four factors, and our engineer may not have enough resources to make even a single obser- vation for each of these combinations. In Chapter 11, we will see how the careful selec- tion of a fraction of these possibilities will usually yield the desired information.
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12 CHAPTER 1 Overview and Descriptive Statistics
EXERCISES Section 1.1 (1–9)
1. Give one possible sample of size 4 from each of the follow-
b. What do you think is the advantage of randomly dividing
ing populations:
the students into the two groups rather than letting each
a. All daily newspapers published in the United States
student choose which group to join?
b. All companies listed on the New York Stock Exchange
c. Why didn’t the investigators put all students in the treat-
c. All students at your college or university
ment group? Note: The article “Supplemental Instruction:
d. All grade point averages of students at your college or
An Effective Component of Student Affairs Programming”
university
(J. of College Student Devel., 1997: 577–586) discusses
2. For each of the following hypothetical populations, give a
the analysis of data from several SI programs.
plausible sample of size 4:
6. The California State University (CSU) system consists of 23
a. All distances that might result when you throw a football
campuses, from San Diego State in the south to Humboldt
b. Page lengths of books published 5 years from now
State near the Oregon border. A CSU administrator wishes to
c. All possible earthquake-strength measurements (Richter
make an inference about the average distance between the
scale) that might be recorded in California during the next
hometowns of students and their campuses. Describe and dis-
year
cuss several different sampling methods that might be
d. All possible yields (in grams) from a certain chemical
employed. Would this be an enumerative or an analytic
reaction carried out in a laboratory
study? Explain your reasoning.
3. Consider the population consisting of all computers of a cer-
7. A certain city divides naturally into ten district neighborhoods.
tain brand and model, and focus on whether a computer
How might a real estate appraiser select a sample of single-
needs service while under warranty.
family homes that could be used as a basis for developing an
a. Pose several probability questions based on selecting a
equation to predict appraised value from characteristics such as
sample of 100 such computers.
age, size, number of bathrooms, distance to the nearest school,
b. What inferential statistics question might be answered by
and so on? Is the study enumerative or analytic?
determining the number of such computers in a sample of
8. The amount of flow through a solenoid valve in an automo-
size 100 that need warranty service?
bile’s pollution-control system is an important characteristic.
4. a. Give three different examples of concrete populations and
An experiment was carried out to study how flow rate
three different examples of hypothetical populations.
depended on three factors: armature length, spring load, and
b. For one each of your concrete and your hypothetical pop-
bobbin depth. Two different levels (low and high) of each fac-
ulations, give an example of a probability question and an
tor were chosen, and a single observation on flow was made
example of an inferential statistics question.
for each combination of levels.
5. Many universities and colleges have instituted supplemental
a. The resulting data set consisted of how many observations?
instruction (SI) programs, in which a student facilitator meets
b. Is this an enumerative or analytic study? Explain your rea-
regularly with a small group of students enrolled in the
soning.
course to promote discussion of course material and enhance
9. In a famous experiment carried out in 1882, Michelson and
subject mastery. Suppose that students in a large statistics
Newcomb obtained 66 observations on the time it took for
course (what else?) are randomly divided into a control group
light to travel between two locations in Washington, D.C. A
that will not participate in SI and a treatment group that will
few of the measurements (coded in a certain manner) were
participate. At the end of the term, each student’s total score
31, 23, 32, 36, 22, 26, 27, and 31.
in the course is determined.
a. Why are these measurements not identical?
a. Are the scores from the SI group a sample from an exist-
b. Is this an enumerative study? Why or why not?
ing population? If so, what is it? If not, what is the rele- vant conceptual population?