Statistics 101: Section L - Laboratory 9
This lab consists of three group activities. For the first activity, you will design an experiment to determine
the optimal cooking time for a new brand of microwave popcorn. For the second activity, you will design an
experiment to determine the effectiveness of the Atkins diet. For the third activity, you will design and
conduct an experiment to determine the average weight of one M&M.
For all activities, keep in mind the three principles of good experiments: control of outside variables,
randomization and replication within the experiment.
Activity 1: Imagine you are employed in the test kitchen of Company Z. Company Z is rolling out a new
line of microwave popcorns. Your group must design an experiment to determine the optimal cooking time
for one of the new brands of microwave popcorn in this new line. The new popcorn will be sold in
individual packages, each with the same label weight. Your task is to design an experiment that will
produce data to help you make an informed decision as to the optimal cooking time for the new brand of
microwave popcorn.
a) First decide on a response. What aspect of the popcorn will help you decide on the optimal cooking
time? How will you measure your response? (Hint: Think about comparing the response between
the individual packages.) Be specific.
b) What are the experimental units for this study? (In other words, what are you conducting the
experiment on?)
c) What is the main factor for this experiment? How many levels of this factor will you include in
your experiment? What are these levels?
d) A secondary factor for this experiment is the wattage of the microwave. Explain how you will
incorporate two different wattage microwaves (700 watts and 1000 watts) into this experiment.
e) What are the treatment groups for your experiment?
f) Come up with a list of outside variables (variables other than the factors) that might affect your
response. How will you control for these variables in your study?
g) How will you incorporate replication in your study?
h) From a statistical point of view more replication is better, e.g. 100 experimental units in each
treatment group. From a practical point of view why might you have less replication, e.g. 10
experimental units in each treatment group?
i) How will you incorporate randomization in your experiment? Be specific about how you will
randomize. From your description, I should be able to perform the randomization.
j) Draw a diagram of your experimental design.
Activity 2: There is considerable debate in the medical community about the benefits of the “Atkins Diet.”
This diet involves eating relatively large amounts of protein and fats and very few carbohydrates. We would
like to design an experiment to compare the weight loss achieved on the Atkins diet with the weight loss
achieved while on a diet based on the USDA food pyramid. There are 100 people available for this
experiment.
a) Who are the experimental units for this experiment? (In other words, who are we conducting the
experiment on?)
b) What is the response variable for this experiment? How will you measure it? Be specific.
c) What is the factor for this experiment? How many levels does the factor have? What are they?
d) How will you incorporate control in this experiment? What are some variables that could influence
the response? How will you control for these variables?
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e) One important characteristic of our subjects that cannot be controlled for is gender. Suppose out of
the 100 people available for this experiment 60 are women and 40 are men. We wish to block on
gender. How will you incorporate replication in a block experiment?
f) How will you incorporate randomization in this experiment?
g) Draw a diagram of your block experimental design.
Activity 3: In a previous lab, we conducted an observational study by selecting Fun Size bags of M&Ms,
weighing the bags and counting the number of M&Ms in each bag. From the analysis of those data, we
found that using least squares regression to predict the weight of an empty bag and the average weight of a
single M&M was not very successful. Part of the problem was that we used data obtained from bags that
contained 20 – 30 M&Ms in each bag, and then tried to use these data to extrapolate back to the origin.
Your task in this activity is to design and conduct an experiment to obtain reasonable estimates of the
average weight of an empty Ziploc bag and the average weight of a single peanut M&M using least squares
regression. You will have a Tupperware container of peanut M&Ms, a Ziploc bag, and a scale to conduct
the experiment. You will put M&Ms in the bag and weigh the bag with the M&Ms on the scale.
a)
b)
c)
d)
e)
What is the response variable for this experiment?
What is the factor for the experiment? What levels of this factor will you use for this experiment?
What are the “treatment” groups for this experiment?
What are the experimental units for this experiment?
What are some outside variables that may affect the response? How will these be controlled in your
experiment?
f) How will you incorporate replication in your experiment? How much replication will you have?
g) How will you incorporate randomization in your experiment? Be specific about how you will
randomize when conducting the experiment.
Before you actually begin to conduct the experiment, check with Nicole or me.
h) Conduct the experiment you have designed. Make sure to record your data.
i) Take your data and complete a regression analysis using JMP. Print off the output and use it to
answer the following questions.
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Describe the relationship between the weight of the bag of M&Ms and the number of M&Ms.
What is the value of the correlation coefficient?
What is the least squares regression equation?
What is the value and interpretation of the slope of the regression equation?
What is the value and interpretation of the y-intercept of the regression equation? Does this
seem correct? Explain briefly.
What is the value and interpretation of R2 for this regression? How good is the prediction of the
weight of the bag and contents using the number of M&Ms?
Describe the residual plot. What does this tell you about the adequacy of the linear model to
approximate the general trend between number and weight?
What is your estimate of the average weight of one peanut M&M based on the regression
analysis?
What is your estimate of the average weight of an empty Ziploc bag based on the regression
analysis?
Why do you think peanut M&Ms were used for this activity instead of plain M&Ms?
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