Assumptions and Conditions
AP Statistics
Assumptions
• Many statistical methods (ex. confidence
intervals, one-proportion z-tests, Bernoulli
trials) are based on important assumptions.
• Those methods cannot be applied or used
unless those conditions are met.
• How do we know if those assumptions are
met? They can be difficult or impossible to
satisfy in certain situations.
Assumptions
Generally, there are three types of Assumptions:
1. Unverifiable: We must simply accept these as
reasonable—after careful thought.
2. Plausible, based on evidence: We test a condition to
see if it is reasonable to believe that the Assumption
is true.
3. False, but close enough: We know the Assumption is
not true, but some procedures can provide very
reliable results even when an Assumption is not fully
met. In such cases, a condition may offer a rule of
thumb that indicates whether or not we can safely
override the Assumption and apply the procedure
anyway.
Assumptions and Conditions
• A condition, therefore, is a testable criterion
that supports or overrides an assumption.
• It is used in types 2 and 3 on previous slide.
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Example
The daily temperatures in Philadelphia
for February are shown to the left. Is
a temperature of 6 degrees
considered unusual?
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Example
The daily temperatures in Philadelphia for
February are shown to the left. Is a
temperature of 6 degrees considered
unusual?
If you were planning to use the Normal
curve and find the z-score, etc. then you
are working under the NORMAL
DISTRIBUTION ASSUMPTION.
In other words, you are assuming that the
population is Normally distributed. Is
it?
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Example
The daily temperatures in Philadelphia for
February are shown to the left. Is a
temperature of 6 degrees considered
unusual?
To see if the population is Normally
distributed (Normal Distribution
Assumption), you must satisfy the
NEARLY NORMAL CONDITION—which
states that the data are roughly
unimodal and symmetric. This can be
done by showing a histogram, normal
probability plot, etc.
Example—Answer (Satisfying of
Condition)
“In order to answer this question, a
Normal Model will be used. The
use of the Normal model,
however, requires the
Assumption of a Normal
Distribution for the population.
Since the distribution of the
population is unknown, we must,
instead, attempt to justify the
Nearly Normal Condition.
The distribution of daily
temperatures in Philadelphia
during February is shown below.
As can be seen, the distribution is
roughly symmetric and unimodalthus satisfying the Nearly Normal
Condition and allowing us to use
the Normal curve to model this
data.”
Assumptions and Conditions for
Inference for a Proportion
Independent Trials Assumption:
 Sometimes we will simply accept this—flipping a
coin, taking foul shots, etc.
 However, if we are trying to make inferences
about a population proportion based on a sample
drawn without replacement, then this assumption
is clearly false. However, we can proceed if we
satsify:
Random Condition
10% Condition
Assumptions and Conditions for
Inference for a Proportion
Normal Distribution Assumption
 Very good chance that this is false—that the
population from which the sample is drawn from
is normal. However, that does not matter if we
can satisfy:
Success/Failure Condition
This can confirm that the sample is large
enough to make the sampling model close
to Normal
Assumptions and Conditions for
“Proportions”
The assumptions and conditions needed for
Inference for a Proportion are the same ones
used for the following “Proportion” methods:
 Sampling Distribution Model for a Proportion
creating a sampling model from a population
 Creating Confidence Intervals for Proportions