Unit 3: Collecting Data Name: KEY

HW 4 – Experimental Design

1) The good folks at Apples Inc want to create bags of presliced apples for kids to easily put in their lunch
boxes. They want to test different mixtures of preservatives (A, B, and C) on their Honeycrisp apples. They will
treat all the apples in a bushel of Honeycrisps by randomly assigning them to each preservation treatment, and
then comparing how long they are able to remain in the bag before they begin to brown.

a) Identify the experimental units, the explanatory and response variables, and the treatments.

Experimental units are the apples, the explantaory variable is the preservative, the response is the time they stay
in the bag before they brown an the treatments are the three types of preservativies (A, B, and C)

b) The researchers plan to use a compltely randomized desgin. Describe how they should assign treatments to
the 126 experimental units.

Label each apple from 1 to 126. Using a random number generator, choose 42 unique numbers. Those 42
numbers correspond to the apples that will go in treatment A. Using a random number generator again, choose
42 new numbers. Ignore numbers that were repeated from the frist round. These numbers will be assigned to
treatment B. The remaining apples will go to treatment C.

c) The researchers suspect that the type of apple will influence how well the preservation method words. They
want to repeat this experiment with 4 different types of apples. Describe how they should change the design of
the experiment to account for this addition.

Because the type of apple will influence how well the preservation method works the best, they should first
block according to apple type. In each block, they should assign the three treatments and compare the results
within each block.

2) A study was conducted to determine if taking a daily dose of aspirin reduces chance of catching the common
cold. This study was conducted using 550 volunteers who were not already on an aspirin regimen. The
subjects were randomly assigned to one of two groups: a treatment group who received a low dose of aspirin
daily, or a control group who received a placebo. The subjects were unaware of what group they were in. At the
end of the study, the subjects were asked to meet with a doctor to discuss if they had any symptoms pertaining
to the common cold.

a) What would be the advantage of having this study b) Describe what the “placebo effect” would look
be double blind? like in this experiment.

By being double blind, both the doctor who was The placebo effect would be a patient getting the
evaluating the patient and the patient themselves did placebo, but believing they got the aspirin, and as a
not know if they received the treatment or the result, ended up reporting that they did not have any
placebo. For the patient, you do not want them to symptoms of a cold because they believed they got
know if they got the aspirin or not, because it could the medicine.
impact how their view the symptoms they get. For
the doctor, you do not want them to know, because
they could interpret the symptoms differently if they
knew what the patient got.
3) A producer brings 130 individuals interested in “dramadies” to serve as an audience for a run through of the
pilot episode for a new Netflix series. There are two lead actors being considered for the starring role in the
show, and each made a pilot for the show. At the end of the run through, the audience members rate the
candidate they watched.

a) Design a completely randomized experiment the TV producer can use.

RA: Label each subject 1
to 130. Using a random
number generator,
Actor 1
generate 65 unique
130 Randomly
Individuals Assign Compare numbers and those
numbers will watch
Actor 2
Actor 1. The remaining
subjects will watch actor
2.

b) Design an experiment where the producer blocks by gender. Then, describe what the benefit of blocking by
gender would be.

RA: In each block, label

Actor 1 each subject 1 to 65.
Randomly
65 Males Compare Using a random number
Assign
Actor 2 generator, generate 33
130
Individuals unique numbers and
Actor 1 those numbers will
Randomly watch Actor 1. The
65 Females Compare
Assign
Actor 2 remaining subjects will
watch actor 2. Repeat for
the second block.

Blocking by gender can let you see how each actor does among the audiences. Depending on who your primary
audience is (male or female), this could help you decide which actor to go with.

4) A group of math teachers in the district are considering a new format for their summative assessments, but
they do not know if students will be more successful on the new format or the old format. They will randomly
assign half of the math students to the new format and half of the students to the old format. There are 204
students.

a) Design a completely randomized experiment the teachers can use.

RA: Put all 204 student names in a
hat. Pull out 102 names and those
names will be assigned to the new
New Format format treatment. The remaining
204 Randomly names will be assigned to the old
Students Assign Compare
Compare
format.
Old Format
b) Design an experiment where the students are blocked by one of the four teachers they have. Then, describe
what the benefit of blocking by teacher would be.

25 Old
51 from Randomly Format
Teacher 1 Assign Compare RA: For the 51 students
26 New
Format with Teacher 1, put all
names in a hat. Pull out 25
25 Old
Format names from the hat and
51 from Randomly
Compare those 25 will be put with
Teacher 2 Assign 26 New the old format. The
204 Format
remaining 26 will go with
Students 25 Old the new format. Repeat this
51 from Randomly Format
Compare process for each of the
Teacher 3 Assign 26 New teacher blocks.
Format
25 Old
51 from Randomly Format
Teacher 4 Assign Compare
26 New
Format

Different teachers have different teaching styles, so some teachers might teach in a way that their students do
better on the new format, while some teachers might teach in a way that they do better on the old format.

3) A marketing team in charge of producing television commercials for children’s products wants to know if
differences in children’s attention span exist among advertisements for different products. The experiment they
conduct uses a sample of 60 children that are 5, 6, or 7-years old. Each child watches one 60-second
commercial for either Product 1, Product 2, or Product 3. Researchers measure the attention span in seconds.

Design a blocked design for this study and describe the benefit of blocking for this experiment.

Product 1 RA: For the 5-year-old block, put

Randomly the names of all the 5-year-olds in a
5 year-olds Product 2 Compare
Assign hat. Randomly select 1/3 of the 5-
Product 3 year-old names and those will be
assigned to Product 1. Of the names
Product 1 that remain, randomly select ½ of
60 Children 6 year-olds
Randomly
Product 2 Compare
the names and those children will be
Assign
assigned to product 2. The
Product 3 remaining children who have not
been selected will be assigned to
Product 1
Product 3. You will repeat this
7 year-olds
Randomly
Product 2 Compare process for the other 2 age groups.
Assign

Product 3

The age of the child could drive how they react to each of the products. Plus, each age has a different natural
attention span, which will affect how each age reacts to the products.