SampleDistributionofMean

SampleDistributionofMean - Suppose that in a company the...

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with the following returns: Stock. ....................... Return A................................. 7% B................................ 12% C................................. -3% D................................ 21% E.................................. 3% In this example, the population mean is equal to 8%, and the population standard deviation is equal to 8.15%. Now, suppose that we decide to take a random sample of three stocks. Assuming that the order is not important and sampling is done without replacement, applying combination equation (n=5, and x=3) there are ten possibilities: Sample Stocks. .............. Returns. ............ Mean 1) A, B, C. ..................... 7%. .12%. .-3%. ..... 5.33% 2) A, B, D. ..................... 7%. .12%. .21%. ...13.33% 3) A, B, E. ..................... 7%. .12%. .3%. ....... 7.33% 4) A, C, D. ..................... 7%. .-3%. .21%. ..... 8.33% 5) A, C, E. ..................... 7%. .-3%. .3%. ....... 2.33% 6) A, D, E. ..................... 7%. .21%. .3%. ..... 10.33% 7) B, C, D. .................... 12%. .-3%. .21%. ....10.00% 8) B, C, E. .................... 12%. .-3%. .3%. ....... 4.00% 9) B, D, E. .................... 12%. .21%. .3%. ..... 12.00% 0) C, D, E. .................... -3%. .21%. .3%. ....... 7.00% As the above example shows, two (or more) samples from the same population will likely have different sample values (mean values ranges from 2.33% to 13.33%), and therefore possibly lead to different decisions. Thus, the sample mean reported to the decision maker in the company will depend on the sample selected, i.e., sample 1, 2, 3,. ....or 10. Note that the sample means (column 3 in the above table) also are different from the population mean, i.e., 8. For example, if sample 4 is selected, the sampling error (the difference between a sample statistic and its corresponding population parameter) is fairly small (8.33 - 8.0 = 0.33), but if the selected sample is sample 2, the error is quite large (13.33 - 8.0 = 5.33). Because the decision maker cannot know how large the sampling error will be before selecting the sample, he/she should know how the possible sample means are distributed. Defination:

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This document was uploaded on 11/25/2011.

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SampleDistributionofMean - Suppose that in a company the...

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