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Unformatted text preview: © 2010 Radha Bose FSU Department of Statistics Central Limit Theorem — 1 Do this before coming to class. (1) Go to http://www.random.org/integers/ . (2) Generate 1 random integer between 1 and 20 and write it down here: __________. This is a sample of size 1. The mean of this sample is the number itself. (3) Now generate 4 random integers between 1 and 20 and write them below. ______________________________ Calculate the mean of your sample of 4: ____________________. (4) Finally, generate 16 random integers between 1 and 20 and write them below. _____________________________________________________________ _____________________________________________________________ Calculate the mean of your sample of 16: ____________________. We will study the distributions of the three means. These distributions are called sampling distributions . Sampling distribution — distribution of all possible values of a statistic obtained from all possible SRSs of the same size drawn from the same population. Statistic — a numerical measurement that describes a characteristic of a sample. Very often sample statistics are used as estimates for the corresponding population parameters. © 2010 Radha Bose FSU Department of Statistics Central Limit Theorem — 2 Information about the histograms below Population: whole numbers 1—20 Popn Mean: 5 . 10 = μ Sample sizes: 1 = n , 4 = n and 16 = n No. of samples: 170 of each type Shape: 1 n = (parent popn) is Uniform , 4 = n and 16 = n are both bellshaped Center: 4 = n and 16 = n are both centered at 5 . 10 = μ (making them unbiased) Spread: less variation as n gets larger Distribution of individual numbers (parent population distribution) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Averages of 1 number (choosing one number at random) © 2010 Radha Bose FSU Department of Statistics Central Limit Theorem — 3 Sampling distribution of 170 sample means when n=4 1 4 4 10 15 28 38 32 27 6 2 1 1 1 20 40 60 80 100 120 [1,2) [2,3) [3,4) [4,5) [5,6) [6,7) [7,8) [8,9) [9,10) [10,11) [11,12) [12,13) [13,14) [14,15) [15,16) [16,17) [17,18) [18,19) [19,20) Averages of 4 numbers (choosing 4 numbers at random) Counts Sampling distribution of 170 sample means when n=16 2 21 117 25 4 1 20 40 60 80 100 120 [1,2) [2,3)...
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This document was uploaded on 10/31/2011 for the course STAT STA2023 at FSU.
 Fall '11
 RADHABOSE
 Central Limit Theorem

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