This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Chapter 6 Sampling and Sampling Distributions A random sample is a set of random variables ,, . . . , (upper case notation) that are: 1 X 2 X n X x identically distributed. That is, each of these random variables has mean P and variance; and 2 V x independently distributed. That is, 0)X,X( Cov j i for any ji . Typically, the population parameters (such as and) are unknown. 2 V Econ 325 Chapter 6 1 A sample of data are the observed numerical outcomes ,, . . . , (lower case notation). The sample mean can be calculated as: 1 x 2 x n x n 1i i x n 1 x Clearly, x will not be identical to the population mean P . For a second sample of n observations denote the numerical outcomes as: ,, . . . , * 1 x * 2 x * n x From this sample the sample mean is: n 1i * i * x n 1 x The two calculated sample means x and * x will be different numbers and neither will be the same as the population mean P . That is, different samples of n observations have different numerical observations and therefore, the calculated sample means are different. Econ 325 Chapter 6 2 The sample mean of the random variables,, . . . , is defined as: 1 X 2 X n X n 1i i X n 1 X X is a linear combination of random variables and, therefore, is also a random variable. X has a probability distribution known as the sampling distribution . The sampling distribution of a sample statistic is the probability distribution of the values it could take over all possible samples of size n drawn from the population. What are the properties of the sampling distribution of X ? First, state the mean: P P )n( n 1 )X(E n 1 X n 1 E)X(E n 1i i n 1i i That is, P )X(E . This says for a large number of samples (say 1000 samples), each with n observations, the average of the calculated sample means will approach the population mean . Econ 325 Chapter 6 3 Now state the variance: n ) n( n 1 )X( Var n 1 X n 1 Var )X( Var 2 2 2 n 1i i 2 n 1i i V V ce independen use Problem: How did the assumption of independence...
View Full
Document
 Spring '10
 WHISTLER
 Economics

Click to edit the document details