One of the earliest applications of the Poisson distribution was made by Student (1907) in studying errors made in counting yeast cells or blood corpuscles with a haemacytometer. In this study, yeast cells were killed and mixed with water and gelatin; the mixture was then spread on a glass and allowed to cool. Four different concentrations were used. Counts were made on 400 squares, and the data are summarized in the following table:

a Estimate the parameter  for each of the four sets of data.

b Find an approximate 95% confidence interval for each estimate.

c Test the goodness of fit of the Poisson distribution to these data using Pearson's chi-square test.

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