M4056 Lecture Notes. September 17, 2010 Some important distributions, continued. Student’s t p and Snedecor’s F p,q Suppose we take samples of size n from a n ( μ, σ 2 ) population. In this case, as we have seen, X-μ σ/ √ n ∼ n (0 , 1) . This serves us well if our intention is to estimate an unknown μ and we know σ . For example, suppose a laboratory instrument measures lengths with a standard error of 0 . 02 millimeters. (In other words, if the same object is measured repeatedly, the readings are normally distributed about the true length, with σ = 0 . 02.) To increase accuracy, we decide to measure each object 25 times and use the average of the 25 readings as our estimate of true length. Homework 1. If 1000 objects are measured in this fashion (requiring 25,000 uses of the instrument), how many are likely to have a true length that is no more than 0 . 01 millimeters from the estimate? But it is unusual to know
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