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# Statistics for Economists ECON 413

UWM

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This 2 page Class Notes was uploaded by Amaya Reilly on Tuesday October 27, 2015. The Class Notes belongs to ECON 413 at University of Wisconsin - Milwaukee taught by Staff in Fall. Since its upload, it has received 13 views. For similar materials see /class/230291/econ-413-university-of-wisconsin-milwaukee in Economcs at University of Wisconsin - Milwaukee.

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Date Created: 10/27/15

ECON 413 Fall 2004 Toward Statistical Inference Statistics is ultimately concerned with drawing inferences about some population of interest We can learn about a population by taking a sample from it and by using the information in the sample to learn about the population There are many different methods of sampling from a population In simple random sampling all possible samples from the population have an equal chance of being the actual sample selected Simple random sampling also gives each member of the population the same chance of being included in the sample Random sampling can be done either with replacement or without replacement Suppose we are interested in learning about a variable X say e g the rate of return on the stock of companies that trade on the New York Stock Exchange NYSE The distribution of the values of X for all companies that trade on the NYSE is called the population distribution If we pick a stock at random from the population of all NYSE stocks the value of X for that stock is a random variable The distribution of this random variable is also the population distribution A random sample of size n is a sequence of independent observations X1X2Xn where X represents the value of X for the ith individual and each X has the distribution of the population being sampled We can write the joint pdf or pf of the observations in a random sample as fOCpxzauaxn fXx1fXxzfyxn where fX denotes the population pdf or pf We are usually interested in learning about certain characteristics of populations that are called parameters For example the mean u and the standard deviation 039 of a population distribution are examples of parameters A parameter is a fixed number Because it is based on all the observations in the population its value is almost always unknown On the other hand a statistic is a numerical descriptive measure of a sample Sample mean X sample median m and sample standard deviation s are examples of statistics Statistics are calculated from the observations in the sample A statistic can be used to estimate an unknown parameter Example A recent survey asked a nationwide random sample of 2500 adults if they agreed or disagreed with the following statement I like buying new clothes but shopping is often frustrating and timeconsuming 66 of he respondents 1650 people out of 2500 agreed ECON 413 Fall 2004 Question What was the population this study aimed to learn about What was the sample What was the parameter of interest What does the number 66 signify Let s denote the proportion of the sample frustrated with shopping by We can use to estimate the proportion of the population that nd shopping for clothes frustrating which we denote by p Question What would happen if we took repeated samples from the population and calculated the sample proportion 7 for each sample Would the value of the statistic remain the same Answer No The value of a statistic changes from sample to sample This is called sampling variability We can examine the values taken by a statistic by constructing a histogram This histogram gives the sampling distribution of the statistic that is the distribution of values taken by the statistic in all possible samples of the same size

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