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Transcript

Section 11.1 Inference About Two Means: Dependent Samples Objective: 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) Work #1 - 4