Chapter 4 Study Guide Solutions
Study Guide
4.1a
4.1b
4.1 MC
Ideal Response
2
The population is all the artifacts discovered at the dig. The sample is those artifacts (2% of the
population) that are chosen for inspection.
4
The population is all 45,000 people who made credit card purchases. The sample is the 137
people who returned the survey form.
6
Letters to legislators are an example of a voluntary response sample—the proportion of letters
opposed to the insurance should not be assumed to be a fair representation of the attitudes of the
congresswoman’s constituents. Only those who have very strong opinions will write in.
8
(a) A voluntary response sample.
(b) It is biased toward readers who feel most strongly about the issue. 85% is probably higher
than the true percent because it is likely that readers who feel most strongly about this issue
have in some way been involved in an accident caused by cell phone use while driving.
18
(a) To obtain an SRS, every tree would need to have an equal chance of being included in the
sample. It is not practical to even identify every tree in the park.
(b) This sampling method is biased because these trees are unlikely to be representative of the
population. Trees along the main road are more likely to be damaged by cars and people
and may be more susceptible to infestation.
(c) The scientists can be confident that the actual percentage of pine trees in the area that are
infected by the pine beetle is near 35% although there is always some error associated with
using sampling to estimate population parameters.
22
(a) Using a stratified random sample would assure the manager that he got opinions from each
type of room. Use each type of view as the strata and randomly pick 60 guests from each
stratum.
(b) A cluster sample would be a simpler option because someone could just slip the forms
under a specific pattern of doors. All rooms ending in a specific number would be the
clusters. For example, all rooms ending in 16. Presumably these are all stacked above each
other on the 30 floors. The manager should just pick two random numbers that represent
rooms on the water side and two random numbers that represent rooms on the golf course
side and then survey all 30 rooms (one per floor) that end in that number.
24
The chance of being interviewed is 3/30 for students over age 21 and 2/20 for students under
age 21. This is 1/10 in both cases. It is not an SRS because not all combinations of students
have an equal chance of being interviewed. For instance, groups of 5 students all over age 21
have no chance of being interviewed.
12
(a) Number the 33 complexes from 01 to 33 alphabetically. Go to the random number table and
pick a starting point. Record two-digit numbers, skipping any that aren’t between 01 and 33
or are repeats, until you have 3 unique numbers between 01 and 33.
(b) Starting at line 117 we read off the following numbers: 38 (ignore), 16, 79 (ignore), 85
(ignore), 32, 62 (ignore), 18. So we have picked: Fairington (16), Waterford Court (32) and
Fowler (18).
15
If you always begin at the same place, then the results would not be random. You would end up
using the same sample in every case.
16
(a) False—if it were true, then after looking at 39 digits, we would know whether or not the
40th digit was a 0.
(b) True—there are 100 pairs of digits 00 through 99, and all are equally likely.
(c) False—0000 is just as likely as any other string of four digits.
37. C
38. D
39. D
40. C
41. E
42. C
Chapter 4 Study Guide Solutions
4.2a
46
(a) This was an observational study because no treatment was imposed on the children. The
researchers simply followed them through their 6th year in school, asking adults to rate
their behavior at several times along the way.
(b) The explanatory variable was the amount of time in child care from birth to age four-and-ahalf. The response variable was the adult ratings of their behavior.
(c) No, this study is an observational study so we cannot make a conclusion of cause and
effect. There could be a lurking variable that is actually causing the difference in adult
ratings of their behavior.
48
(a) This is an example of an observational study. The researchers did not assign people to
either use or not use cell phones.
(b) No, this study is an observational study so we cannot make a conclusion of cause and
effect.
50
One possible lurking variable is level of academic motivation. Those who drink may have less
academic motivation leading to lower grades. So if students do not do well, we are not sure if it
is because of the alcohol itself or if it is simply a matter of lower level of academic motivation.
58
There was no control group for comparison purposes this year. Over a year, many things can
change: the state of the economy, hiring costs (due to an increasing minimum wage or the cost
of employee benefits), etc. In order to draw conclusions, we would need to make the $500
bonus offer to some people and not to others during the same time frame, and compare the two
groups.
60
(a) Write all names on slips of paper, put them in a container and mix thoroughly. Pull one slip
out and note the name on it. That person gets assigned treatment 1. Pull another name out
and assign that person to treatment 2. The third person gets assigned treatment 3. Keep
rotating through the treatments until all have been assigned.
(b) Assign the students numbers between 001 and 150. Pick a spot on Table D and read off the
first 25 numbers between 001 and 150, skipping any that aren’t between 001 and 120 or are
repeats. These are assigned to treatment 1. The next 25 numbers read are assigned to
treatment 2. Keep doing this until all people have been assigned to one of the 6 treatments.
(c) Assign the students numbers between 001 and 150. Using the RandInt function on the
calculator, and ignoring all repeats, assign the first 25 numbers chosen to treatment 1, the
next 25 to treatment 2, and so on.
62
(a) This is a completely randomized design. The outline is given below:
(b) Assign the plots the labels 01 through 18. Write the labels on 18 identical slips of paper, put
them in a hat, and mix them well. Draw out 6 slips. The corresponding plots will be in
Group 1. Draw out 6 more slips. These plots will be in Group 2, and the remaining 6 plots
will be in Group 3.
65
(a) The principle of experimental design that is violated here is random assignment. If players
are allowed to choose which treatment they get, those who choose one particular treatment
over the other may be different in a fundamental way. For example, maybe the weaker
players will be more likely to choose the new method and the stronger players would stick
with weight lifting.
(b) The response variable of the number of push-ups that a player can do could be part of what
the coach should measure, but this only measures one kind of upper-body strength and he
should probably combine this with other measures as well.
Chapter 4 Study Guide Solutions
4.2b
71
Because the experimenter knew which subjects had learned the meditation techniques, he (or
she) may have had some expectations about the outcome of the experiment: if the experimenter
believed that meditation was beneficial, he may subconsciously rate that group as being less
anxious.
73
(b) The difference in the percent of women who received acupuncture and became pregnant
and those who lay still and became pregnant was large enough to conclude that the
difference was most likely due to the treatments rather than to chance.
74
(b) The difference in weight loss seen was large enough to conclude that the difference was
most likely due to the treatments rather than to chance.
78
(a) The blocks are the sexes. The cancer reacts differently to treatments in men and women so
we want to eliminate sex as a lurking variable. We want to test all three types of treatments
in both men and women.
(b) If we used a completely randomized design, we could end up with a treatment that is given
much more frequently to one of the two sexes. Then we will not know if any differences we
see between that treatment and the others are due to the treatment itself, or the fact that
cancer reacts differently in women than men.
(c) If the researchers had only 800 men and no women, we would not have to have a block
design. We could just randomly assign the treatments to the subjects. Unfortunately, we
would only be able to make conclusions about how the treatments work in men.
80
(a) A randomized block design would be better in this case to control for the lurking variable of
initial weight. A completely randomized design could assign several of the more
overweight subjects to the same weight-loss treatment. If these subjects lost much more
weight than subjects receiving the other treatments, researchers wouldn’t know if it was due
to the treatment or to subjects’ initial weights.
(b) The blocks should be based on how overweight the subjects are so that the subjects within a
block are as similar as possible. If we block on last name, there will be potentially many
differences between the people in a block.
(c) Ordered by increasing weight, the five blocks are (1) Williams-22, Deng-24, Hernandez-25,
and Moses-25; (2) Santiago-27, Kendall-28, Mann-28, and Smith-29; (3) Brunkenstein-30,
Obrach-30, Rodriguez-30, and Loren-32; (4) Jackson-33, Stall-33, Brown-34, and Cruz-34;
(5) Birnbaum-35, Tran-35, Nevesky-39, and Wilansky-42. The exact randomization will
vary with the starting line in Table D. Different methods are possible; perhaps the simplest
is to number the subjects from 1 to 4 within each block, then assign the members of block 1
to a weight-loss treatment, then assign block 2, etc. For example, starting on line 133, we
assign 4-Moses to treatment A, 1-Williams to B, and 3-Hernandez to C (so that 2-Deng gets
treatment D), then carry on for block 2, etc.
81
(a) If all rats from litter 1 were fed diet A and we found diet A to be better, we would not know
if this was because of the diet itself, or because that rat strain was different from the other
rat strain. This is what it means for the strain and the diet to be confounded. We cannot
separate out the effects of one variable from the effects of the other.
(b) A better design would be a randomized block design with the strains as the blocks. In this
case, each diet would be given to some rats of each strain.
83
(a) This is a completely randomized design.
(b) Have the students be the blocks (or more specifically, matched pairs, where each student is
his/her own matched pair). Have each student drive the simulator twice – once with a
hands-free cell phone and once without, in random order.
(c) So that we are not measuring an order effect – that the students are better at the driving
simulator the second time no matter what the treatment is.
Chapter 4 Study Guide Solutions
84
4.2 MC
(a) This was a matched pairs design because each volunteer got each treatment in a random
order.
(b) The investigators chose this type of design over a completely randomized design because
they recognized that each individual would have different characteristics to their blood
vessels. This way they can directly compare the blood flow with and without the bittersweet
chocolate under the same conditions (in the same body).
(c) It is important to randomize the order of the treatments for each subject so that we are not
measuring a time effect. We want to make sure that any effect we see is due to the
chocolate and not to the time at which we measured it.
91. C
92. A
93. B
94. D
95. C
96. D
97. C
98. B