9-5 Resampling: Using Technology for Inferences 497 Bootstrapping and Randomization – Two Samples Access tech supplements, videos, and data sets at www.TriolaStats.com TECH CENTER continued TI-83, 83 84 Plus Calculator 8 us Ca cu ato Not available. R R command not available at time of publication. R is rapidly evolving, and an updated list of statistical commands is available at TriolaStats.com. Excel Not available. Statistical Literacy and Critical Thinking 1.Bootstrapping and Randomization When resampling data from two independent samples, what is the fundamental difference between bootstrapping and randomization? 2.Sampling Methods A student obtains a sample of responses to the question “Do you plan to take or have you taken a statistics course?” A second student obtains a sample of responses to the same question. The first student surveys only males at the same college, and the second student surveys only females at the same college. What is wrong with the samples? Can randomization be used to overcome the flaws of those samples? 3.Randomization with Commute Times Given the two samples of commute times (minutes) shown here, which of the following are randomizations of them? Boston: 5 10 25 30 45 New York: 10 20 60 a. Boston: 10 10 60. New York: 5 20 25 30 45. b. Boston: 10 10 60 20 25. New York: 5 30 45. c. Boston: 5 10 25 25 60. New York: 5 30 30 60. d. Boston: 10 10 60. New York: 5 20 25 30 45. e. Boston: 10 10 10 10 10. New York: 60 60 60. 4.Randomization vs t Test Two samples of commute times from Boston and New York are randomly selected and it is found that the samples sizes are n1 = 8 and n2 = 12 and each of the two samples appears to be from a population with a distribution that is dramatically far from normal. Which method is more likely to yield better results for testing m1 ≠ m2: Hypothesis test using the t distribution (as in Section 9-2) or the resampling method? Two Proportions. In Exercises 5–8, use (a) randomization and (b) bootstrapping for the indicated exercise from Section 9-1. Compare the results to those obtained in the original exercise. 5.Exercise 7 in Section 9-1 “Buttered Toast Drop” 6.Exercise 8 in Section 9-1 “Tennis Challenges” 7.Exercise 9 in Section 9-1 “Cell Phones and Handedness” 8.Exercise 10 in Section 9-1 “Denomination Effect” 9-5 Basic Skills and Concepts
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