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

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```d. Report (again) the observed class value of the statistic. (What proportion of students
in your class put Timâs name on the left?)
pÌ =
e. Calculate how many standard deviations the observed class value of the statistic is
from the hypothesized mean of the null distribution, 0.5. In other words, subtract the
0.5 from the observed value, and then divide by the standard deviation. This is the
standardized statistic
z = (observed statistic pÌ â 0.5) / SD of null distribution.
f.
Once you calculate this value, you interpret it as âhow many standard deviations the
observed statistic falls from the hypothesized parameter value.â What strength of
evidence against the null does your standardized statistic provide?
g. How closely does your evaluation of strength of evidence based on the standardized
statistic compare to the strength of evidence based on the p-value in #4c?
Guidelines for evaluating strength of evidence from standardized values of statistics
Standardizing gives us a quick, informal way to evaluate the strength of evidence against the
null hypothesis:
between -1.5 and 1.5:
below -1.5 or above 1.5:
below -2 or above 2:
below -3 or above 3:
little or no evidence against the null hypothesis;
moderate evidence against the null hypothesis;
strong evidence against the null hypothesis;
very strong evidence against the null hypothesis.
Step 5: Formulate conclusions.
6. Now, letâs step back a bit further and think about the scope of inference. We have found
that in most classes, the observed data provide strong evidence that students do better
than random guessing which face is Timâs and which is Bobâs. In that case, do you think
that most students at your school would agree on which face is Timâs? Do you think this
means that most people can agree on which face belongs to Tim? Furthermore, does
this mean that all people do ascribe to the same facial prototyping? We will look more at
the scope of inference in chapters 2 and 4.
June 27, 2014
MAA PREP workshop
27
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