Question

Most of our problems will start off with a statement like "Let Xi,..., Xn be a random sample from the that assumption is reasonable, other times it isn't. We can sometimes use simulation, together with known illustrate this, consider the following sample of bay anchovy larvae counts taken from the Hudson River: 158, distribution." However, this distributional assumption is often just that, an assumption. Sometimes properties of the assumed distribution, to check whether our distributional assumption is reasonable. To 143. 106. 57. 97. 80. 109. 109. 350. 224. 109. 214. 84 (d) The question remains, how should we expect S2 to behave if the data really do arise from a Poisson distribution? To answer this question, we can carry out a simulation. We want our simulated data sets to mimic the one collected. So, we'll generate data sets of size n = 13, since that was the sample size of the original data. In addition, we'll simulate the data sets assuming they come from a Poisson distribution with λ = 2, since that's our best guess at the parameter. In your favorite simulation software (Excel works! So does R. SAS, Matlab, ), generate 100 data sets each with n 13 observations (e) For each data set, calculate S2. Construct a histogram of your 100 simulated S2 values. (g) Where does the s2 from the original data set fall on this histogram? How many of the simulated S2 values are greater than the observed s2? (h) What does this lead you to believe about the Poisson assumption? Is it reasonable in this case? What is your reasoning?

Answer 1