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Special Case: Paired Sample T-Test

Special Case: Paired Sample T-Test. Examples Paired-sample? Car Radial Belted 1 ** ** Radial, Belted tires 2 ** ** placed on each car. 3 ** ** 4 ** ** Person Pre Post 1 ** ** Pre- and post-test

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Special Case: Paired Sample T-Test

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  1. Special Case: Paired Sample T-Test Examples Paired-sample? • Car Radial Belted 1 ** ** Radial, Belted tires 2 ** ** placed on each car. 3 ** ** 4 ** ** • Person Pre Post 1 ** ** Pre- and post-test 2 ** ** administered to each 3 ** ** person. 4 ** ** • Student Test1 Test2 1 ** ** 5 scores from test 1, 2 ** ** 5 scores from test 2. 3 ** ** 4 ** **

  2. Example* Nine steel plate girders were subjected to two methods for predicting sheer strength. Partial data are as follows: GirderKarlsruheLehighdifference, d 1 1.186 1.061 2 1.151 0.992 9 1.559 1.052 Conduct a paired-sample t-test at the 0.05 significance level to determine if there is a difference between the two methods. * adapted from Montgomery & Runger, Applied Statistics and Probability for Engineers.

  3. Example (cont.) Hypotheses: H0: μD = 0 H1: μD ≠ 0 t__________ = ______ Calculate difference scores (d), mean and standard deviation, and tcalc … d = 0.2736 sd = 0.1356 tcalc = ______________________________

  4. What does this mean? • Draw the picture: • Decision: • Conclusion:

  5. Goodness-of-Fit Tests • Procedures for confirming or refuting hypotheses about the distributions of random variables. • Hypotheses: H0: The population follows a particular distribution. H1: The population does not follow the distribution. Examples: H0: The data come from a normal distribution. H1: The data do not come from a normal distribution.

  6. Goodness of Fit Tests (cont.) • Test statistic is χ2 • Draw the picture • Determine the critical value χ2 with parameters α, ν = k – 1 • Calculate χ2 from the sample • Compare χ2calcto χ2crit • Make a decision about H0 • State your conclusion

  7. Tests of Independence • Hypotheses H0: independence H1: not independent • Example Choice of pension plan. 1. Develop a Contingency Table

  8. Example 2. Calculate expected probabilities P(#1 ∩ S) = _______________ E(#1 ∩ S) = _____________ P(#1 ∩ H) = _______________ E(#1 ∩ H) = _____________ (etc.)

  9. Hypotheses • Define Hypotheses H0: the categories (worker & plan) are independent H1: the categories are not independent 4. Calculate the sample-based statistic = ________________________________________ = ______

  10. The Test 5. Compare to the critical statistic, χ2α, r where r = (a – 1)(b – 1) for our example, say α = 0.01 χ2_____ = ___________ Decision: Conclusion:

  11. Homework for Wednesday, Nov. 10 • pp. 319-323: 25, 27 • Pp. 345-346: 12, 13

  12. Homework

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