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Toxicity experiment. In an experiment testing the effect of a toxic substance, 1,500 experi- mental insects were divided at random into six groups of 250 each. The insects in each group were exposed to a fixed dose of the toxic substance. A day later, each insect was observed Death from exposure was scored 1, and survival was scored 0. The results are shown below; Xj denotes the dose level (on a logarithmic scale) administered to the insects in group j and Y.j denotes the number of insects that died out of the 250 (nj) in the group. 2 4 5 250 28 2 250 53 250 93 4 250 126 250 172 6 250 197 Logistic regression model (14.20) is assumed to be appropriate a. Plot the estimated proportions pj nj against Xj. Does the plot support the analyst's belief that the logistic response function is appropriate? b. Find the maximum likelihood estimates of Ao and B1. State the fitted response function c. Obtain a scatter plot of the data with the estimated proportions from part (a), and super- impose the fitted logistic response function from part (b). Does the fitted logistic response function appear to fit well? d. Obtain exp(bi) and interpret this number. e. What is the estimated probability that an insect dies when the dose level is X 3.5? f. What is the estimated median lethal dose-that is, the dose for which 50 percent of the experimental insects are expected to die?

Answer 1