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Unformatted text preview: Introduction Definitions Estimation Hypothesis Testing Confidence Intervals Econ 103, UCLA, Fall 2010 Introduction to Econometrics Lecture 2: Review of Statistics Sarolta Lacz September 28, 2010 Introduction Definitions Estimation Hypothesis Testing Confidence Intervals Introduction Steps of empirical analysis: 1 Formulate the question of interest 2 Obtain data 3 Estimate the parameter(s) of interest 4 Conduct statistical inference Introduction Definitions Estimation Hypothesis Testing Confidence Intervals Outline Definitions  population, random sampling Estimation Unbiased estimator Consistent estimator Central Limit Theorem Hypothesis testing How to do hypothesis testing Small vs. large samples pvalues 2sided and 1sided tests Confidence intervals Introduction Definitions Estimation Hypothesis Testing Confidence Intervals Definitions/1 Statistics can be used to study economic variables, e.g. yearly wages of adults in the US. Population : group of interest, e.g. all adults in the US Y : random variable of interest, e.g. yearly wage for a randomly selected adult Population Distribution of Y : describes how Y varies (or is distributed) across the population. Typically we do not observe the whole population, only a subset of it, a sample . Introduction Definitions Estimation Hypothesis Testing Confidence Intervals Definitions/2 Random Sample : values of Y for a set of n randomly chosen adults from the population. ( Y 1 ,...,Y n ) is a random sample of size n . It also means that each individual of the population gets to be part of the sample with the same probability. Y i and Y j represent two observations in the sample, which are themselves random variables. Since Y i and Y j are values of Y , they have the same distribution as Y . In particular, E ( Y i ) = E ( Y j ) = Y V ar ( Y i ) = V ar ( Y j ) = 2 Y Because of random sampling, any two different observations in the sample are independent. Y i and Y j are independently and identically distributed (i.i.d.) . Introduction Definitions Estimation Hypothesis Testing Confidence Intervals The importance of random sampling Before the 1936 Presidential elections, a poll conducted over the phone was published, indicating that Alf M. Landon would defeat D. Roosevelt by 57% to 43% . The election was indeed a landslide. But Roosevelt won 59% to 41%. Introduction Definitions Estimation Hypothesis Testing Confidence Intervals Estimation/1 Problem: we typically dont observe the moments of the population distribution, e.g. we dont know Y , mean wages in the US....
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This note was uploaded on 10/13/2010 for the course ECON 101 taught by Professor Buddin during the Spring '08 term at UCLA.
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