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# L15posted_rev1 - Data and Random Variables At the start of...

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Unformatted text preview: Data and Random Variables At the start of this course we discussed varia- tion in data. Suppose that there are two meth- ods of making concrete aggregates, an existing one (denoted by symbol A ), and a new one, (denoted by B ), which contains a new binding agent. It is desired to determine whether the strength of the new concrete is greater than that of the old. Ten blocks are made from each and the strength tested of each block. 1 Let x 1 ,...,x 10 and y 1 ,...,y 10 be the measured strengths of ten sample blocks of each aggre- gate. These are the data. The { x i } and { y i } will vary because of random variations in raw material. There will also be a possible sys- tematic difference between the { x i } and { y i } each set taken as a whole, because of the ef- fect of the binding agent. Even if the binding agent is effective (positive), it is not necessar- ily the case that all the { y i } will exceed all the { x i } because random variations may overcome the positive increase in strength. Additionally, these ten measurements are only one possi- ble sample of size ten from each method. We could equally have made ten other blocks from each method. In fact, in order to arrive at a conclusion, we would need to understand the effect of random variations on the sample data we obtained. 2 The difference ¯ y- ¯ x is determined by an infinity of values of ¯ x and an infinity of values of ¯ y. In turn the ¯ x values are determined by an infin- ity of x i values, each of which comes from the same population, and represents the strength...
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L15posted_rev1 - Data and Random Variables At the start of...

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