Modeling the proliferation of E. coli in farm animals is critical to a safe food supply. The article “Ecological and Genetic Determinants of Plasmid Distribution in E. coli” (Environ. Biol. 2016: 4230–4239) describes a study of bacterial replication in grazing cattle with low frequencies of antibiotic-resistant genes. The following data is provided on X = number of replicons for 527 bacterial isolates:

a. The article’s authors examined whether X follows a Poisson distribution. Use the data to determine the maximum likelihood estimate of the parameter μ.
b. Perform a χ² test at the .05 significance level by treating the last category as “
4” so that the hypothesized probabilities sum to 1. Refer back to Example 13.9.

Example 13.9

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No. of replicons Frequency 0 139 1 184 2 154 3. 34 4 16