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

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6. In case of discrepancy between the simulation-based p-value and the normal
approximation-based p-value, which do you think would be the more reliable?
7. (Optional) Notice that the applet provides you with an option to report the Exact Binomial
p-value. Check on the option, and report the resulting p-value: ___________________.
8. (Optional) Which p-value is closer to the Exact Binomial p-value: the simulation-based pvalue (from #2) or the normal approximation-based p-value (from #4)?
Figure 1.2 shows a few examples of null distributions.
Figure 1.2: Null distributions for various studies. A bell-shaped distribution, called a normal
distribution, can be used to nicely approximate some of them, but will not work well for others.
St. George’s
(n = 10; 𝜋 = 0.15)
St. George’s
(n = 361; 𝜋 = 0.15)
Halloween treats
(n = 283; 𝜋 = 0.5)
The St. George’s (n = 361) and Halloween treats (n = 283) simulations show bell-shaped
curves. However, the first sample of St. George’s heart patients (n = 10) is a not bell-shaped
curve, in part because the distribution is not symmetric and in part because there are so few
values that the sample proportion can be.
June 27, 2014
MAA PREP workshop
37