Chap10-Introduction-to-Estimation

Chap10-Introduction-to-Estimation - 1 Chap 10: Intro to...

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1 CHAPTER 10: INTRODUCTION TO ESTIMATION Stats & Prob. for Bus. Mgmt (Stat1100) Jochem Chap 10: Intro to Estimation b Overview/Goals b 1. Understand the 2 Types of Estimators b 2. Be able to estimate the Population Mean when the Population Standard Deviation is known 2 b 3. Be able to Determine the appropriate Sample Size 3 Chap 10: Intro to Estimation b 0. Where we left off Population & Parameters Individual Member of Population Probability distribution Chap 6-8 Population & Parameters Sample Statistics Sampling distribution Population & Parameters Sample Statistics Sampling distribution Chap 9 4 Chap 10: Intro to Estimation b 1. Types of Estimators b Point Estimator s Estimates the value of an unknown parameter through a single value/point. s Problems: s 1. it is unlikely (in fact, the probability is 0) that an estimator that is based on a sample that is smaller than the population has the exact same value as a continuous statistic. s 2. We have no information about how close the estimator is to the true parameter. s 3. Point estimators do not reflect the greater accuracy that originates from an increasing sample size.
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5 Chap 10: Intro to Estimation b 1. Types of Estimators b Interval Estimator s Using an interval as an estimation to an unknown parameter (e.g., “ μ lies in between 50.3 and 50.7”). 6 Chap 10: Intro to Estimation b 1. Concepts of Estimation b 3 desirable Characteristics for an Estimator s 1. Unbiasedness s If we repeatedly drew samples from the population, then for each sample it is equally likely that the estimate is above or below the true parameter. B expected value of an unbiased estimator across many samples is equal to the true parameter. 7 Chap 10: Intro to Estimation b 1. Concepts of Estimation b 3 desirable Characteristics for an Estimator s 1. Unbiasedness s If we repeatedly drew samples from the population, then for each sample it is equally likely that the estimate is above or below the true parameter. B expected value of an unbiased estimator across many samples is equal to the true parameter. s 2. Consistency s the difference between the estimator and the parameter grows smaller as the sample size increases. 8 Chap 10: Intro to Estimation b 1. Concepts of Estimation b 3 desirable Characteristics for an Estimator s 1. Unbiasedness s If we repeatedly drew samples from the population, then for each sample it is equally likely that the estimate is above or below the true parameter. B expected value of an unbiased estimator across many samples is equal to the true parameter. s
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This note was uploaded on 03/26/2012 for the course STAT 1100 taught by Professor Chiappetta during the Spring '08 term at Pittsburgh.

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Chap10-Introduction-to-Estimation - 1 Chap 10: Intro to...

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