Solutions Manual for Fundamental Statistics for the Behavioral ...

Student Manual for Fundamental Statistics for the Behavioral Sciences (7th
edition) David C. Howell
The University of Vermont
Contents Chapter 1 Introduction
Chapter 2 Basic Concepts
Chapter 3 Displaying Data
Chapter 4 Measures of Central Tendency
Chapter 5 Measures of Variability
Chapter 6 The Normal Distribution
Chapter 7 Basic Concepts of Probability
Chapter 8 Sampling Distributions and Hypothesis Testing
Chapter 9 Correlation
Chapter 10 Regression
Chapter 11 Multiple Regression
Chapter 12 Hypothesis Tests Applied to Means: One Sample
Chapter 13 Hypothesis Tests Applied to Means: Two Related Samples
Chapter 14 Hypothesis Tests Applied to Means: Two Independent Samples
Chapter 15 Power
Chapter 16 One-way Analysis of Variance
Chapter 17 Factorial Analysis of Variance
Chapter 18 Repeated-Measures Analysis of Variance
Chapter 19 Chi-Square
Chapter 20 Nonparametric and Distribution-Free Statistical Tests
Chapter 21 Choosing the Appropriate Analysis
Preface The purpose of this manual is to provide answers to students using the
accompanying text, Fundamental Statistics for the Behavioral Sciences, 7th
ed. I have provided complete answers to all of the odd-numbered questions.
I am often asked for answers to even-numbered exercises as well. I do not
provide those because many instructors want to have exercises without
answers. I am attempting to balance the two competing needs. You may find on occasion that you do not have the same answer that I do.
Much of this will depend on the degree to which you or I round off
intermediate steps. Sometimes it will make a surprising difference. If your
answer looks close to mine, and you did it the same way that I did, then
don't worry about small differences. It is even possible that I made an
error. I know that there will be errors in some of these answers. There always
are. Even the most compulsive problem solver is bound to make errors, and
it has been a long time since anyone accused me of being compulsive. I do
try, honest I do, but something always slips past-sometimes they even slip
past while I am correcting another error. So I maintain a page on the web
listing the errors that I and other have found. If you find an error (minor
and obvious typos don't count unless they involve numbers), please check
there and let me know if it is a new one. Some classes even compete to see
who can find the most errors-it's rough when you have to compete with a
whole class. The address for the main web page, is http://www.uvm.edu/~dhowell/fundamentals/ , and the link to the Errata is
there.
Important note: Due to the way hypertext links are shown by Microsoft
Word, the underlining often obscures a single underline character, as in
"More_Stuff." If you see a space in an address, it is often really a "_."
Chapter 1-Introduction
1.1 A good example is the development of tolerance to caffeine. People who
do not normally drink caffeinated coffee are often startled by the effect
of one or two cups of regular coffee, whereas those who normally drink
regular coffee see no such effect. To test for a context effect of
caffeine, you would first need to develop a dependent variable measuring
the alerting effect of caffeine, which could be a vigilance task. You could
test for a context effect by serving a group of users of decaffeinated
coffee two cups of regular coffee every morning in their office for a
month, but have them drink decaf the rest of the time. The vigilance test
would be given shortly after the coffee, and tolerance would be seen by an
increase in errors over days. At the end of the month, they would be tested
after drinking caffeinated coffee in the same and in a different setting. The important points here are:
1. Tolerance is shown by an increase in errors on the vigilance task.
1. To see the effect of context, subjects need to be presented with
caffeine in two different contexts.
2. There needs to be a difference between the vigilance performance in
the two contexts.
1.3 Contexts affects people's response to alcohol, to off-color jokes, or
to observed aggressive behavior. 1.5 The sample would be the addicts that we observe.
1.7 Not all people in the city are listed in the phone book. In
particular, women and children are underrepresented. A phone book is
particularly out of date as a random selection device with the increase in
the use of cell phones. Many telephone surveys really miss the general population, and instead
focus on a restricted population, dominated by male adults.
1.9 In the tolerance study discussed in the text, we really do not care
what the mean length of paw-lick latency is. No one would be excited to
know that a mouse can stand on a surface at 105 degrees for 3.2 seconds
without licking its paws. But we do very much care that the population mean
of paw-lick latencies for morphine-tolerant mice is longer in one context
than in another. 1.11 I would expect that your mother would continue to wander around in a
daze, wondering what happened. 1.13 Three examples of measurement data: performance on a vigilance task;
typing speed, blood alcohol level. 1.15 Relationship: The relationship between stress and susceptibility to
disease; the relationship between driving speed and accident rate. 1.17 You could have one group of mice trained and tested in the same
condition, one group trained in one condition and tested in the other, and
a group given a placebo in the training context but given morphine in the
testing condition.
1.19 This is an Internet search exercise without a fixed answer. The
Statistics Homepage is an online statistics text. Various departments offer
data sets, computing advice, and clarifying examples. Chapter 2-Basic Concepts
2.1 Nominal: names of students in the class; Ordinal: the order in which
students hand in their first exam; Interval: the student's grade on that
first exam; Ratio: the amount of time that the student spent studying for
that exam. 2.3 If the rat lies down to sleep in the maze, after performing
successfully for several trials, this probably says little about what the
animal has learned in the task. It may say more about the animals level of
motivation.
In this exercise I am trying to get the students to see that there is
often quite a difference between what you and I think our variable is
measuring and what it actually measures. Just because we label
something as a measure of learning does not make it so. Just because
the numbers increase on a ratio scale (twice as much time in the maze)
doesn't mean that what those numbers are actually measuring is ratio
(twice as much learning). 2.5 We have to assume the following at the very least (and I am sure I
left out some)
1. Mice are adequate models for human behavior.
1. Morphine tolerance effects in mice are like heroin tolerance
effects in humans,
2. Time on a warm surface is in some way analogous to a human response
to heroin.
3. A context shift for mice is analogous to a context shift for
humans.
4. A drug overdose is analogous to pain tolerance.
2.7 The independent variables are the sex of the subject and the sex of
the other person. 2.9 The experimenter expected to find that women would eat less in the
presence of a male partner than in the presence of a female partner. Men,
on the other hand, were not expected to vary the amount that they ate as a
function of sex of their partner.
2.11 We would treat a discrete variable as if it were continuous if it had
many different levels and were at least ordinal. 2.13 When I drew 50 numbers 3 times I obtained 29, 26, and 19 even numbers,
respectively. For my third drawing only 38 percent of my numbers were even,
which is probably less than I might have expected-especially if I didn't
have a fair amount of experience with similar exercises. 2.15 Eyes level condition:
a) X3 = 2.03; X5 = 1.05; X8 = 1.86
b) SX = 14.82
c) [pic] 2.17 Eyes level condition:
a) (SX)2 = 14.822 = 219.6324; SX2 = 1.652 + ... + 1.732 = 23.22
b) SX/N = 14.82/10 = 1.482
c) This is the mean, a type of average.
The above answers are the variance and standard deviation of Y. You
really aren't going to do much more calculation that this.
2.19 Putting the two sets of data together:
a) Multiply pairwise
b) SXY = 22.27496
c) SXSY = 14.82*14.63 = 216.82
d) ?XY ? ?X?Y. They do differ, as you would expect.
e) [pic]
2.21 X 5 7 3 6 3 SX = 24
X + 4 9 11 7 10 7 S(X + 4) = 44 = (24 + 5*4) 2.23 In the text I spoke about room temperature as an ordinal scale of
comfort (at least up to some point). Room temperature is a continuous
measure, even though with respect to comfort it only measures at an ordinal
level. 2.25 The Beth Perez story:
a) The dependent variable is the weekly allowance, measured in dollars
and cents, and the independent variable is the sex of the child.
b) We are dealing with a selected sample-the children in her class.
c) The age of the students would influence the overall mean. The fact
that these children are classmates could easily lead to socially
appropriate responses-or what the children deem to be socially
appropriate in their setting.
d) At least within her school, Beth could randomly sample by