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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 6 Comments • These notes cover material from Chapter 6, Sections 6.1-6.4, 6.6. They are not complete . I will do a lot of calculations on blackboard. • I’m planning to spend two lectures on this material. • MINITAB will be used to illustrate confidence intervals. Rafal Kulik 1 MAT2378 Probability and Statistics for the Natural Sciences Chapter 6 Point estimation Statistical inference consists of methods used to make conclusions about a population based on a random sample . In particular, we want to estimate an unknown parameter , say θ , using a single number called point estimate . This point estimate is obtained using a statistics , which is simply a function of a random sample. The probability distribution of statistics is called sampling distribution . Rafal Kulik 2 MAT2378 Probability and Statistics for the Natural Sciences Chapter 6 Example: If we want to estimate the parameter μ (the population mean), we may take a random sample Y 1 ,...,Y n and compute a statistics Y . In other words, ¯ Y is the point estimate of μ . We have learned that Y has normal distribution if the population is normal, or approximately normal distribution, if n is big. Therefore, the sampling distribution of ¯ Y is normal. Example: If we want to estimate parameter σ 2 (the population variance), we may take a random sample Y 1 ,...,Y n and compute a statistics S 2 = 1 n- 1 ∑ n i =1 ( Y i- ¯ Y ) (the sample variance). In other words, S 2 is the point estimate of σ 2 . Example: Soybean example p. 179. Rafal Kulik 3 MAT2378 Probability and Statistics for the Natural Sciences Chapter 6 Variance of the estimator and standard error If data Y 1 ,...,Y n come from a population with mean μ and variance σ 2 , then Var( Y ) = σ 2 /n . Thus Standard error of the Mean : σ Y = σ √ n ....

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