ch13 - Ch 13 1 2 3 4 5 6 7 1

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1 Ch 13 The Accuracy of Averages • We now turn to estimate the accuracy of an  average  computed from a simple random sample. • We wish to know how much variability there is in the  average numbers drawn from a box. • Assume a box model as follows: 1 2 3 4 5 6 7
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2 • We make 25 draws at random with replacement and  got: 2 4 3 2 5 7 5 6 4 5 4 4 1 2 4 4 6 4 7 2 7 2 5 7 3 • The SUM of the numbers is _______, so their  AVERAGE is _______ . • The SUM of the numbers is _______, so their  AVERAGE is _______ . • The SUM of the draws is subject to chance  variability, therefore the AVERAGE is too. • The new problem is to calculate the expected value  and SE of the AVERAGE. • Let’s say we make another 25 draws at random with  replacement and got: 5 1 4 3 4 5 2 1 7 7 1 2 3 2 4 7 1 6 5 3 6 6 3 3 4
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3 Example 1 25 draws are made at random with replacement from the box: # draws 1 2 3 4 5 6 7 The average of the draws will be about _____ , give or take  ______ or so. SOLUTION) The average of the BOX is 4, so the AVERAGE of the  draws should be around 4. The give-or-take number is the SE. To get the SE for the  AVERAGE, we need to go back to the SUM. The expected value of the SUM is (number of draws X average of  box) = 25 X 4 = 100. The SD of the box is 2, and the SE for the SUM is     (                   X SD of box) =       X 2 = 10. The SUM will be 100, give or take 10 or so. 25
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4 What does this say about the average? If the SUM is one SE above the expected value, or 100+10, the  AVERAGE of 25 draws is  (100+10)/25 = 100/25 + 10/25 = 4 + 0.4 On the other hand, if the SUM is one SE below the expected value,  or 100-10, the AVERAGE of 25 draws is          (100-10)/25 = 100/25 - 10/25 = 4 - 0.4 So, the AVERAGE of the draws will be about 4, give or take 0.4 or  so. That is, 4 is the expected value for the average of the draws, and 0.4  is the SE. I N
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This note was uploaded on 03/14/2010 for the course ECON Statistics taught by Professor Yy during the Spring '10 term at Seoul National.

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ch13 - Ch 13 1 2 3 4 5 6 7 1

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