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Note for ECON 2370 at UH

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This 3 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 14 views.

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Date Created: 02/06/15
Inferences from Small Samples 1 U The Central Limit Theorem which describes the mean standard deviation and shape of the sampling distribution depends on large samples n 2 30 What can be said about the mean standard deviation and shape of the sampling distribution when n is small If the sample is drawn from approximately normal populations the mean of the sampling distribution is the same for the sampling distribution of the means for large sample The shape is symmetric The standard deviation is not 1 it varies because the shape varies for different sample sizes Student s T scores distribution 1 2 Developed by WS Gosset in 1908 Based on a ratio of the standard normal distribution function and the square root of the X2 distribution 3 Given a sample of n observations the statistics j 8 has a t distribution with n 1 degrees of freedom If 1 There are many different If distributions 2 Every distribution resembles a standard normal distribution but each have fatter tails 3 Small samples have more variability 4 As the sample size approaches 30 the distribution becomes normal Degrees of Freedom 1 Number of independent units of observations in the sample relevant to estimation of a particular point estimate 2 There are n observations as the initial units of information 3 Only one observation is used to determine the point estimate 4 The remaining observations are allowed to be any value they are allowed to be free Mathematica Examples How do T scores compare to Z scores Here are the two tailed values at p005 Z Scores 196 TScores 1129 2045 df20 2086 1115 2131 1110 2228 if 5 2571

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