Download Introduction to Chance Models (Section 1.1) Introduction A key step

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Step 4: Draw inferences beyond the data
Because I want to focus on the right front tire, I will make the variable binary (right front or not)
and the parameter of interest in this study is the long-run probability that a Cal Poly student
picks the left front tire. What symbol should I use to refer to this unknown parameter value:
p̂ , 𝜋, 𝑥̅ , 𝜇, 𝜎, s, n – copy and paste below.
(g) Restate the hypotheses in terms of this parameter.
(h) Is the sample proportion who selected the left front tire greater than one-fourth? (If not,
there’s no need to conduct a simulation analysis. You will have no evidence that this tire is
selected more than one-fourth of the time in the long run.)
(i) Simulate: Use the One Proportion applet to simulate 1000 repetitions of this study,
assuming that every student in class has a 0.25 probability of selecting the right front tire.
For your simulation
“Success” represents:
“Chance of success” =
One repetition =
(j) Using the proportion of successes for the values on the horizontal axis, what is the center of
your null distribution? Does it make sense that this is the center? Explain.
(k) Strength of evidence: Determine the p-value from your simulation results. Also interpret
what this p-value probability represents (i.e., the long-run proportion of what that do what
assuming what?!).
(l) Evaluate this p-value: Does this p-value provide strong evidence against the null hypothesis?
(m) Determine and interpret the standardized statistic from your simulation analysis.
Standardized statistic =
observed statistic  hypothesized parameter
=
standard deviation of null distributi on
(n) According to this standardized statistic, is the observed value of the sample proportion
surprising when the null hypothesis is true? Is this consistent with what the p-value told you?
June 27, 2014
MAA PREP workshop
31
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