2.11.10_Lec 10

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

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 An estimator of a population parameter: a An estimator of a population parameter: a statistic (e.g., sample mean, sample proportion) An estimate of a population parameter: the value of the estimator for a particular sample Interval estimation Interval estimation A point estimate plus an interval that expresses the uncertainty or variability associated with the estimate 3 1.2 Statistical Inference: Testing Hypothesis Test Given the observed data, do we reject or accept a pre-specified null hypothesis in favor of an alternative? 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 1 2 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 (contd) We know the sampling distribution of these statistics, e.g. (If is not known, we can use s, the sample standard deviation, as a point estimator of ) ( ) 2 ~ , , w h e r e X X X X N n = Useful for: Interval estimation Hypothesis testing 7 2. 1 Point Estimation by the Method of Maximum Likelihood Maximum Likelihood Estimate (MLE) is the value of , call it , that makes the observed data maximally likely to have occurred (Fisher, 1925) A great moment in the history of science. l 8 5 2.1 Point Estimation by the Method of Maximum Likelihood (contd) ( ) ( ) 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....
View Full Document

Page1 / 17

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

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online