rmins_lab_4 - IOE 265 Fall 07 Lab 4 Probability Plots Note...

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IOE 265 – Fall 07 October 11, 2007 Note: Please make sure you type in your answers in the spaces provided and submit this file electronically via the CTools website under Assignments. Save this file as ‘ uniqname _lab_4’ with your own uniqname. If you are given a data set, the conclusions you make about the parameters of the underlying distribution of that data (we’ll get into this beginning chapter 7) depend heavily upon whether the underlying distribution is normal or not. The question, then, is whether or not the data comes from a normal distribution. How can you tell? There are several sophisticated statistical tests that one can apply, none of which we’ll learn in IOE 265. There is a simpler test called a normal probability plot (or Q-Q plot). Probability plots can be made for many probability distributions. For our purposes, we’ll focus on creating and using them for normal distributions. The general idea is this: plot the observed data against the percentiles of a normal distribution. If the plot appears like straight, perhaps with a mild S-shape, then the data likely comes from a normally distributed population. If there is a strong non-linear pattern, then the data is likely from a non-normal underlying distribution. Here’s how to generate a normal probability plot. a) Rank the data from smallest to largest. b) Assuming there are n observations, generate the [100( i - .5)/ n ] th z -percentiles for i = 1,2, …, n . In other words, if there are 10 observations, find the 5 th z -percentile (-1.645), 15
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