AP Statistics
Chapter 13 Notes
Two-sample problems
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The goal is to compare the responses of two
treatments given to randomly assigned groups,
or to compare the characteristics of two
populations.
We will be using rules for combining
independent variables that we discussed in
chapter 7.
Two Sample t-test/t-interval
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1. Hypotheses
H0: μ1 = μ2
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OR
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H0: μ1 - μ2 = 0 Ha: μ1 - μ2 > < ≠ 0
*It is possible that μ1 - μ2 = something other
than 0, but that is rare.*
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Ha: μ1 > < ≠ μ2
2 Sample t-test/interval
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2. Conditions
(a) Randomness (SRS). If you are comparing
two populations, then you must have two
separate SRS’s. If you are doing an experiment,
the subjects must be randomly assigned to
groups.
(b) Normality: Same as before, but you must
check for both populations/groups.
2 sample t-test/interval
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2. Conditions continued….
(c) Independence: The samples must have no
influence on each other. If you are working
with two separate populations, then you can
apply the N > 10n rule.
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In order to verify conditions, you need to analyze
how the data was collected.
2-sample t-test/t-interval
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3. Calculations
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4. Conclusion
2 proportion z interval
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*Normality n1(p-hat1), n1(1 - p-hat1),
n2(p-hat2), and n2(1 - p-hat2) must all be greater
than 5.
2 proportion z test
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What will the hypotheses look like?
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is the combined sample proportion
=count of successes in both samples combined /
count of individuals in both samples combined
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