2.11.10_Lec 10

# 2.11.10_Lec 10 - 1 Lecture 10 Concepts of Estimation and...

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Unformatted text preview: 1 Lecture 10 Concepts of Estimation and Hypothesis Testing Lecture 10 1 Hypothesis Testing Lecture 10 Outline 1. Two Methods for Statistical Inference • Estimation Estimation • Hypothesis Testing 2. Point Estimation 3. Confidence Interval Estimation 4. Hypothesis Testing 5. Review of Estimation and Hypothesis Testing 2 2 1.1 Statistical Inference: Estimation • Point estimation ¾ An estimator of a population parameter: a ¾ An estimator of a population parameter: a statistic (e.g., sample mean, sample proportion) ¾ An estimate of a population parameter: the value of the estimator for a particular sample • Interval estimation Interval estimation ¾ A point estimate plus an interval that expresses the uncertainty or variability associated with the estimate 3 1.2 Statistical Inference: Testing • Hypothesis Test ¾ Given the observed data, do we reject or accept a pre-specified null hypothesis in favor of an alternative? ¾ “Significance testing” 4 3 1.3 Statistical Inference: Search for “Truth” Sampling distribution Observed Value Truth for for a Population Representative Sample Parameter Statistic = Point estimate (calculated from the data) Statistical inference- Interval estimate- Hypothesis testing 5 2. Point Estimation 1 X 1 2 X X − 1 μ 1 2 μ μ − is a point estimator of is a point estimator of l 1 p l l p p 1 p p p − is a point estimator of is a point estimator o 6 1 2 p p − 1 2 p p is a point estimator of 4 2. Point Estimation (cont’d) • We know the sampling distribution of these statistics, e.g. (If σ is not known, we can use s, the sample standard deviation, as a point estimator of σ ) ( ) 2 ~ , , w h e r e X X X X N n σ μ σ σ = • Useful for: ¾ Interval estimation ¾ Hypothesis testing 7 2. 1 Point Estimation by the Method of Maximum Likelihood • Maximum Likelihood Estimate (MLE) is the value of μ , call it , that makes the observed data maximally likely to have occurred • (Fisher, 1925) A great moment in the history of science. l μ 8 5 2.1 Point Estimation by the Method of Maximum Likelihood (cont’d) ( ) ( ) 7 3 10 1 3 L p p p ⎛ ⎞ = − ⎜ ⎟ ⎝ ⎠ 9 Figure: Graph of likelihood of different proportion parameter values for a binomial process with X = 3 and n = 10 0.3 3. Confidence Interval3....
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2.11.10_Lec 10 - 1 Lecture 10 Concepts of Estimation and...

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