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Chapter 11 (Sp12)

Chapter 11 (Sp12) - Section 11.1 Inferences from Matched...

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Section 11.1 – Inferences from Matched Pairs A sampling method is independent when the individuals selected for one sample do not dictate which individuals are to be in the second sample. A sampling method is dependent (matched pairs) when the individuals selected to be in one sample are used to determine the individuals in the second sample. Requirements : 1. Sample data consist of dependent matched pairs 2. Samples are simple random samples 3. The number of matched pairs is greater than 30 or differences are normally distributed. d = individual difference between two values in a matched pair d = mean value of the differences d for the paired sample data (average of “ x y ” values) s d = standard deviation of the differences d for the paired sample data n = number of pairs of data μ d = mean value of the differences d for the population of paired data Hypotheses : H o : μ d = 0 H 1 : μ d 0 or μ d > 0 or μ d < 0 WE WILL ONLY CONSIDER THE TEST STATISTIC AND P-VALUE IN THIS CHAPTER. YOU WILL NOT HAVE TO DRAW A PICTURE!! TEST STATISTIC and P-VALUE come from the calculator. Hints: •If you want L 1 to be bigger than L 2 (ie L 1 > L 2 ), do a right-tailed test. μ d > 0 •If you want L 1 to be smaller than L 2 (ie L 1 < L 2 ) do a left-tailed test. μ d < 0 STAT, TESTS, T-Test (#2) µ 0 will be 0 Select “Data” Choose L 3 Enter “before” data in L 1 . Enter “after” data in L 2 . Go to the title bar of L 3 and make L 3 = L 1 – L 2 1

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Example : In low-speed crash test of five BMW cars, the repair costs were computed for a factory authorized repair center and an independent repair center. Is there sufficient evidence at α = 0.01 to support the claim that the independent center has lower repair costs? Authorized repair center \$797 \$571 \$904 \$1147 \$418 Independent repair center \$523 \$488 \$875 \$911 \$297 I. H o : H 1 : II. α = III. T.S. = t = IV. P-value = V. Reject H o or Do Not Reject H o VI. (conclusion) 2
Example : A researcher wanted to compare the pulse rates of identical twins to see whether there was any difference. Eight sets of twins were selected. At α = 0.05, is there enough evidence to support the claim that there is a difference in the pulse rates of twins?

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Chapter 11 (Sp12) - Section 11.1 Inferences from Matched...

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