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Alternative Values for Probability of Success
(adapted from Chapter 1 Investigation)
Background: A legendary story on college campuses concerns two students who miss a
chemistry exam because of excessive partying but blame their absence on a flat tire. The
professor allowed them to take a make-up exam, and he sent them to separate rooms to take it.
The first question, worth five points, was quite easy. The second question, worth ninety-five
points, asked: Which tire was it?
Wednesday we collected data from you, asking which of the four tires you would pick if you
were caught in this situation (and had to make up a tire on the spot). For some reason, I
conjecture that college students appear to have a tendency to pick the
tire. You will
use these data to conduct a test of whether the sample data provide convincing evidence that
this tire is picked more often than we would expect if the four tires were picked equally often
(purely at random).
Step 1: Ask a research question
(a) Identify the research conjecture.
Step 2: Design a study and collect data
(b) What are the observational units?
(c) What is the variable that is measured/recorded on each observational unit? (Hint: State as a
binary variable.)
(d) Describe the parameter of interest in words.
(e) State the null and alternative hypotheses to be tested.
Null hypothesis (H0) >>
Alternative hypothesis (Ha) >>
Step 3: Explore the data
Fill in the tallies of your responses.
Front left
Front right
Back left
Back right
Total
(f) Calculate the observed statistic: What proportion of students selected the left front tire? How
many students participated? (Include the symbols you would use to represent these value
(copy and paste one of these symbols below: p̂ , 𝜋, 𝑥̅ , 𝜇, 𝜎, s, n)
June 27, 2014
MAA PREP workshop
30
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