93 Construct a probability plot that will allow you to

Last updated: 10/19/2023

93 Construct a probability plot that will allow you to assess the plausibility of the lognormal distribution as a model for the rainfall data of Exercise 83 in Chapter 1 EXERCISE 83 FROM CHAPTER 1 83 Consider numerical observations x x It is frequently of interest to know whether the x s are at least approxi mately symmetrically distributed about some value If n is at least moderately large the extent of symmetry can be assessed from a stem and leaf display or histogram However if n is not very large such pictures are not par ticularly informative Consider the following alternative Let y denote the smallest x y the second smallest x and so on Then plot the following pairs as points on a two dimensional coordinate system y x X Y 1 X X y y 2 X X There are n 2 points when n is even and n 1 2 when n is odd a What does this plot look like when there is perfect symmetry in the data What does it look like when observations stretch out more above the median than below it a long upper tail b The accompanying data on rainfall acre feet from 26 seeded clouds is taken from the article A Bayesian Analysis of a Multiplicative Treatment Effect in Weather Modification Technometrics 1975 161 166 Construct the plot and comment on the extent of symmetry or nature of departure from symmetry 4 1 7 7 17 5 31 4 32 7 40 6 92 4 115 3 118 3 119 0 129 6 198 6 200 7 242 5 255 0 274 7 274 7 302 8 334 1 430 0 489 1 703 4 978 0 1656 0 1697 8 2745 6