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Abstract:
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In this poster, we explore an Advanced Placement Statistics Problem (#4, 2006 free response exam) which is a classic two-sample comparison of means. We briefly present the published solution and then critique the assumptions on which it is built, especially the assumption that independent random samples were taken. We use standard probability tools and simulation work to address these questions about the independence assumption: (i) Were the samples really independent? (ii) How does this assumption affect the methods used to obtain the published solution? (iii) Were the sample means uncorrelated? (iv) Are the results from the classical methods reliable? This example offers multiple classroom activities for student exploration of: sampling distributions, distinction between random variables which are independent and those which are uncorrelated, and simulation work.
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