mat2378-Chapter5 - MAT2378 Rafal Kulik Version 2009/Oct/17...

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Unformatted text preview: MAT2378 Rafal Kulik Version 2009/Oct/17 Rafal Kulik MAT2378 Probability and Statistics for the Natural Sciences Chapter 5 Comments These notes cover material from Chapter 5, Sections 5.1-5.3. They are not complete . I will do a lot of calculations on blackboard. Im planning to spend two lectures on this material. MINITAB will be used to illustrate Central Limit Theorem. Rafal Kulik 1 MAT2378 Probability and Statistics for the Natural Sciences Chapter 5 Sampling variability Recall: Some characteristics of a sample may be thought as approximation to the true characteristics of the population (e.g., relative frequency histogram approximates the density curve, the sample mean and sample variance approximate the population mean and variance, respectively). How good is such approximation? To answer this, we have to consider sampling error , which in turn is related to sampling variability . A probability distribution that characterizes some aspects of sampling variability is called a sampling distribution . Example 5.1. Rafal Kulik 2 MAT2378 Probability and Statistics for the Natural Sciences Chapter 5 Sampling Distribution - dichotomous observation Assume that we have a coin such that p = P (HEAD) = 0 . 3 , but we do not know this value of p . Flip this coin twice. If Y is the number of heads, and p is the proportion of heads, then the sampling distribution is Y p Probability . 7 . 7 = 0 . 49 1 1/2 . 7 . 3 + 0 . 3 . 7 = 0 . 42 2 1 . 3 . 3 = 0 . 09 The meaning of the above table is the following: if we repeat the above experiment many times, in 42% cases the proportion of heads will be 1/2....
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This note was uploaded on 01/13/2010 for the course MAT MAT2378 taught by Professor Kulik during the Spring '09 term at University of Ottawa.

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mat2378-Chapter5 - MAT2378 Rafal Kulik Version 2009/Oct/17...

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