Calculate the likelihood ratio for Example B of Section 9.5 and compare the results of a...

Calculate the likelihood ratio for Example B of Section 9.5 and compare the results of a test based on the likelihood ratio to those of one based on Pearson’s chi-square statistic

Reference

Bacterial Clumps

In testing milk for bacterial contamination, 0.01 ml of milk is spread over an area of 1 cm² on a slide. The slide is mounted on a microscope, and counts of bacterial clumps within grid squares are made. The Poisson model appears quite reasonable for the distribution of the clumps at first glance: The clumps are presumably mixed uniformly throughout the milk, and there is no reason to suspect that the clumps bunch together. However, on closer examination, two possible problems are noted. First, bacteria held by surface tension on the lower surface of the drop may adhere to the glass slide on contact, producing increased concentrations in that area of the film. Second, the film is not of uniform thickness, being thicker in the center and thinner at the edges, giving rise to nonuniform concentrations of bacteria. The following table, taken from Bliss and Fisher (1953), summarizes the counts of clumps on 400 grid squares.