# Lecture21 - ECO220Y Lecture 21 Introduction to Estimation...

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ECO220Y Lecture 21 troduction to Estimation Introduction to Estimation igiwa anaka Migiwa Tanaka Reading: pp.305-307, section 10.1, 10.2

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Outline asic Steps in Statistical Analysis Basic Steps in Statistical Analysis Estimation Definition: Estimation, Estimator & Estimate. Types of Estimators Properties of Estimators Estimation of μ when σ 2 is known Point Estimation terval Estimation (continues to lecture 22) Interval Estimation (continues to lecture 22)
Basic Steps in Statistical Analysis lanning tatistical Inference Planning Form Statistical Inference Research Question Collect Estimation Theory robability Theory Data Hypothesis Probability Theory Distribution of Random Variables Descriptive Analysis of Testing Data

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Statistical Inference tatistical Inference: Draw a conclusion about a population Stat st ca e e ce: aw a co c us o about a popu at o using information of randomly selected sample from the population. Two methods: Estimation : Estimate the value of population parameter on the basis of observed/collected data. Example: stimate the mean of the length of telephone conversation (monthly) in Estimate the mean of the length of telephone conversation (monthly) in Ontario. Estimate the median income in Canada Hypothesis Testing Formulate a specific hypothesis about the population (parameter), then use an evidence in a sample to decide if it is true. Example of hypothesis: The distribution of the length of telephone conversation in Ontario is normal. The median income in Canada is greater than \$60,000.
Estimation stimator function of a sample drawn randomly Estimator A function of a sample drawn randomly from a population. xample: Example: As an estimator of population mean, use sample mean. r estimators of population arameters rresponding sample For estimators of population parameters, corresponding sample statistics are natural candidates. an estimator random variable? Is an estimator random variable? Estimate – The numerical value of estimator when a ecific sample is applied to it specific sample is applied to it. The sample mean is 50. Is an estimate random variable?

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Types of Estimation oint Estimation btaining a number from computations Point Estimation Obtaining a number from computations on the observed values of the random variable. he number= an approximation of unknown population parameter The number an approximation of unknown population parameter. Example: Proportion of heads in n coin toss=0.5 Interval Estimation – Obtaining an interval defined by two umbers from computations on the observed values of the numbers from computations on the observed values of the random variable.
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Lecture21 - ECO220Y Lecture 21 Introduction to Estimation...

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