By Edward C. Bryant

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**Example text**

We can never actually determine the true average, however, so we must settle for an estimate based upon the sample observations. When we consider the problem of estimating the population average, may tell us to use as an estimate the average of the sample our intuition observations. discuss This in is, an excellent estimate, and we fact, shall some of its properties. were in grade school, " learned to compute the average by adding up the figures to be averaged and dividing by the number of figures added.

Suppose we have the following Y values: 10, 7, 8, 9, 10. We make the following identification: Yi The order = in 10, F2 = 7, F3 = 2F; = 10 8, F4 = 9, F6 = +7+8+9+ 10 Then 10. = 44 which computations are performed is important. example, - 10 2 + 72 + 82 + 92 + 10 2 = 394 For 42 Statistical Analysis but (SF = 2 t) 44 2 - from That is, to subtract 10 them up. - S(F, 10) 2 = (10 - Also, the formula 2(F; each Y, then to square the results, 1,936. - 10) 2 + - (7 10) + 2 - (8 2 (O) -0 + EXERCISE4-2. Z(F 2 Yi t + + 9 (-3) + 2 + 2 (-2) 4+1+0= + (-1) + Compute Y for the above and nSF 2 - (2F) 2 data.

If he draws a sample of 10 items and grades them, what region of rejection will he Suppose one sis is choose? The answer obviously will depend upon a, the risk he is willing to run of rejecting a true hypothesis, but it is also dependent upon the alternatives he wishes to guard against. 6), then clearly he must reject the stated hypothesis number of grade A units in his sample is either very small or very if the large. However, if he is concerned only with guarding against the alternatives in which p is greater than p he will reject p only if the observed number of grade A units is very high.