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Section 11.1 Inference About Two Means: Dependent Samples
Distinguish between independent and dependent sampling; test hypotheses
regarding matched pairs data.
A sampling method is independent when the individuals selected for one sample do not
dictate which individuals are in a second sample.
 Randomly divide seniors into two groups then test using different curriculums.
 Randomly divide patients into two groups and test a new medication giving one
group the new drug the other group a placebo.
A sampling method is dependent when the individuals selected for one sample are used to
determine the individuals in the second sample. Dependent samples are often referred to
as matched-pairs samples.
 Compare salaries of married couples.
 Compare dexterity of dominant versus nondominant hand.
Test Hypotheses Regarding Matched-Pairs Data
Inference on matched-pairs data use the same methods as inference on a single population
mean with  unknown, except that the differences are analyzed.
To test hypotheses regarding the difference of two means using a matched-pairs design,
the following requirements must be satisfied.
 A simple random sample is obtained
 The sample data are matched pairs
 The differences are normally distributed with no outliers or the sample size, n, is
large, n  30
Hypothesis Tests Using TI-83/84, Two-Sample t-Tests, Dependent Sampling
1. If necessary, enter raw data in L1 and L2. Let L3  L1  L2 (or L3  L2  L1 ),
depending on how the alternative hypothesis is defined.
2. Press , highlight TESTS, and select 2: T-Test
3. If the data are raw, highlight DATA; make sure that List is set to L3 and Freq is 1.
If summary statistics are known, highlight STATS and enter the summary statistics.
For the value of  0 , enter the value of the mean stated in the null hypothesis.
4. Select the direction of the alternative hypothesis.
5. Highlight Calculate and press 
Confidence Intervals
Follow the same steps given for hypothesis tests, except select 8: TInterval. Also, select
a confidence level (such as 95% = 0.95)
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