STATISTICS 402 - Assignment 2
Solution
1. Chapter 1: Review Exercises (pgs. 34-37) # 3, 4, 5, and 8.
#3
a) chance error
b) bias
c) chance error
#4
a) False
b) False
c) True
d) True
e) True
f) False
g) False
h) Sort of true. For a random sample, each set of n individuals has
the same chance of being the sample chosen as every other set of n
individuals.
#5
a) The population average is equal to 3.0.
b) The five possible values for random error are; –2, –1, 0, +1, and +2.
c) The random error of 0 is most likely (twice as likely as any of the
others).
d) i. The average of the sample is 2.0.
ii. “B. The difference between the sample average and population
average is due to chance errors that come from the method of sampling.”
Correct.
#8
Random assignment of conditions to material reduces the chance of a
bias due to an uncontrolled variable. Random assignment provides
the basis for formal statistical inference.
2. For each of the following descriptions, answer the following questions using
complete sentences. Also comment if the experiment is fine as described or flawed.
If flawed, how can it be fixed?
 What is the response?
 What are the conditions of the study (i.e. treatments)?
 What is the experimental material? What are the experimental units?
 What are the outside variables that are controlled? Is there a control group?
If so, explain what the control group is.
 Are treatments randomly assigned to the experimental units? Is experimental
material randomly selected from a larger population?
 Is there replication within the experiment?
 Is the experiment fine as described or is it flawed. If flawed, how can it be
fixed?
1
a) A study was done with 644 cancer patients receiving chemotherapy at one of
several cancer treatment centers across the United States. All the patients had
suffered nausea in a previous round of chemotherapy even though they were
given standard anti-nausea medicines. Patients were given one of three doses of
ginger (the equivalent of ½ gram, 1 gram or 1 ½ grams of ginger per day) or
dummy capsules that contained no ginger. The amount of ginger each patient
received was determined at random so that 161 patients got each amount of
ginger. All patients were given standard anti-nausea medicines in addition to the
ginger or no ginger. Patients took the medicines and ginger/no ginger for six
consecutive days, beginning three days before chemotherapy. Each day
participants reported the amount of nausea they were experiencing on a scale from
0 (no nausea) to 10 (extreme nausea).






The response is the amount of nausea as reported on a scale of 0 to 10.
The conditions of the study are the four levels of ginger; 0 g/day, ½ g/day,
1 g/day and 1 ½ g/day.
The experimental material consists of the 644 cancer patients. The
experimental units are the individual cancer patients.
There are several outside variables that are controlled. All patients are
receiving chemotherapy. All patients have had nausea in the past. All
patients are given standard anti-nausea medicines in addition to the
ginger. The group that gets 0 g/day of ginger is the control group.
The amount of ginger each patient gets is determined at random.
Patients come from cancer centers across the United States but there is no
mention of random selection.
There is replication within the experiment with 161 patients in each
treatment group (level of ginger).
The experiment is fine as long as the random assignment of levels of ginger is
done correctly. One way to do this is to assign a unique number from 1 to
644 to each of the patients. Using JMP, create a column labeled Ginger and
put 0 in the first 161 rows, ½ in the next 161 rows, 1 in the next 161 rows and
1 ½ in the next 161 rows. Create another column labeled Patient. Use
Formula – Random – Col Shuffle to randomly mix the numbers from 1 to
644. Each row indicates the treatment (amount of ginger) that is randomly
assigned to which patient number.
b) Some salmon sold in grocery store fish markets is “farm raised.” Salmon
“farming” involves hatching salmon from eggs in fresh water tanks and letting
them grow for 12 to 18 months. The young salmon are then transferred to cages
suspended in the ocean where they are fed for another year or two before
harvesting. The salmon are usually fed pellets made from fishmeal. However,
using fishmeal in this way raises environmental concerns because natural
occurring fish populations are depleted to make the fishmeal. A company
proposes to use soybean meal as a partial substitute for fishmeal but salmon
farmers are concerned that this might affect the weight of salmon at harvest time.
2
An experiment is proposed to compare pellets made of 100% fishmeal with
pellets made of 75% fishmeal and 25% soybean meal and with pellets made of
50% fishmeal and 50% soybean meal. Because it is difficult to keep track of
individual salmon, only the final weight of salmon at harvest will be recorded.
For the experiment, 300 young salmon are selected at random from the hundreds
of thousands of young salmon in the fresh water tanks. Those 300 young salmon
are then divided into three groups at random. One group of 100 will be put in an
ocean cage and fed pellets made of 100% fishmeal. Another group of 100 will be
put in another ocean cage and fed pellets made of 75% fishmeal and 25% soybean
meal. The third group of 100 will put in a third ocean cage and fed pellets made
of 50% fishmeal and 50% soybean meal. Which type of pellets a group of 100
salmon gets is determined at random. Each ocean cage is given the same amount
of pellets each time the salmon are fed. Feeding is done at the same time each
day for all the ocean cages. After one year in the ocean cages, the salmon are
harvested and weighed.






The response is the weight of the salmon after one year in the ocean
cages.
The conditions of the study are the three types of food; 100% fishmeal,
75% fishmeal/25% soybean meal and 50% fishmeal/50% soybean meal.
The experimental material consists of the 300 salmon. The experimental
unit is an ocean cage containing 100 salmon.
There are several variables that are controlled. Each ocean cage is given
the same amount of food. Feeding is done at the same time of day. All
salmon are harvested after 1 year. The 100% fishmeal could be
considered a comparison group because that is what the current practice
is.
Which type of pellets a group of 100 salmon gets is determined at
random. The salmon are randomly selected from a larger population
consisting of hundreds of thousands of salmon.
There is no replication within the experiment because only one ocean
cage is used for each type of food.
The experiment is flawed because there is no replication of the treatments.
Only one ocean cage is used for each type of food. There is no way of
determining if changes in weight are due to the type of food or the other
conditions in the ocean cages (e.g. ocean cages could have different water
temperatures). To fix this there needs to be several ocean cages for each type
of food. The type of food must be randomly assigned to the ocean cages.
c) One theory regarding memory states that verbal material is remembered as a
function of the degree to which it was processed when it was initially presented.
To test this theory an experiment is run with 100 college students selected at
random from all those students enrolled in psychology courses at a large
university. Each student will use one of five methods to memorize a list of words.
3
The method a student will use is determined by rolling a fair die once for each
student. The number on the upper most face of the die indicates the method.
1. The Counting method involves reading a list of words and counting the
number of letters in each word.
2. The Rhyming method involves reading a list of words and thinking of words
that rhyme with each word on the list.
3. The Adjective method involves reading a list of words and thinking of
adjectives that modify the words, one adjective for each word.
4. The Imagery method involves reading a list of words and forming vivid
images for each word.
5. The Standard method involves reading a list of words and no other
instructions are given.
6. Roll the die again.
Once a method has 20 students assigned it can no longer be assigned thus assuring
there are 20 students for each method. All students are given the same list of 30
words. All students are given 15 minutes to read the list, employing the method
given to them. After 15 minutes the list is taken away and students are asked to
write down all the words they can remember. The number of words correctly
recalled is noted for each student.






The response is the number of words correctly recalled.
The conditions of the study are the five methods; Counting, Rhyming,
Adjective, Imagery and Standard.
The experimental material consists of the 100 college students. The
experimental units are the 100 students.
The outside variables that are controlled are the list of words (all students
get the same list of 30 words) and the time to memorize the list is the same
for all students. The students using the Standard method could be
considered a “control” group.
The 100 students are randomly selected from the larger population of all
students taking psychology courses at the university. The method of
memorization is assigned at random to students using a fair die.
There is replication within the experiment by having 20 students for each
method of memorization.
The experiment is flawed in using a stopping rule (once 20 students are
assigned a method it can no longer be assigned) when assigning methods to
students. Instead, a completely random assignment should be used.
Random assignment: Put 100 poker chips (20 white, 20 red, 20 blue, 20
purple and 20 yellow) in a box and mix thoroughly. Have each student in the
experiment pick a poker chip, without replacement, from the box. Students
with white chips use the Counting method. Students with red chips use the
Rhyming group. Students with blue chips use the Adjective method.
Students with purple chips use the Imagery method. Students with yellow
chips use the Standard method.
4