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

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steadily. He then watched to see what Doris would do. After looking at the light, Doris swam
near the curtain and began to whistle loudly. Shortly after that, Buzz whistled back and then
pressed the button on the right—he got it correct and so both dolphins got a fish. But this single
attempt was not enough to convince Dr. Bastian that Doris had communicated with Buzz
through her whistling. Dr. Bastian repeated the process several times, sometimes having the
light blink (so Doris needed to let Buzz know to push the left button) and other times having it
glow steadily (so Doris needed to let Buzz know to push the right button). He kept track of how
often Buzz pushed the correct button.
In this scenario, even if Buzz and Doris can communicate, we don’t necessarily expect Buzz to
push the correct button every time. We allow for some “randomness” in the process; maybe on
one trial Doris was a bit more underwater when she whistled and the signal wasn’t as clear for
Buzz. Or maybe Buzz and Doris aren’t communicating at all and Buzz guesses which button to
push every time and just happens to guess correctly once in a while. Our goal is to get an idea
of how likely Buzz is to push the correct button in the long run.
Figure 1.1: Depending whether or not the light was blinking or shown steadily, Doris had to
communicate to Buzz as to which button to push.
Let’s see how Dr. Bastian was applying the Six-Step Statistical Investigation Method.
Step 1: Ask a research question. Can dolphins communicate in an abstract manner?
Step 2: Design a study and collect data. Notice Dr. Bastian took some time to train the
dolphins in order to get them to a point where he could test a specific research conjecture. The
research conjecture is that Buzz pushes the correct button more often than he would if he and
Doris could not communicate. If Buzz and Doris could not communicate, Buzz would just be
guessing which button to push. The observational units are Buzz’s attempts and the variable for
each attempt is whether or not on each attempt, Buzz pushes the correct button (a categorical
Step 3: Explore the data. In one phase of the study, Dr. Bastian had Buzz attempt to push the
correct button a total of 16 different times. In this sample of 16 attempts, Buzz pushed the
correct button 15 out of 16 times. To summarize these results, we report the statistic, a
numerical summary of the sample. For this example, we could report either 15, the number of
correct pushes, or 15/16 = 0.9375, as the statistic.
Definitions: The set of observational units on which we collect data is called the sample. The
number of observational units in the sample is the sample size. A statistic is a number
summarizing the results in the sample.
June 27, 2014
MAA PREP workshop