Notice that this exercise is very similar to the example where we fit the Poisson to the births data. There is a handout after the lecture on the Poisson where that exercise is explained. You had to complete it for the review exercise. Doing one more example will allow you to solidify what you did there.

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Do extinctions occur randomly through the long fossil's record of Earth's history?, or are there periods in which extinction rates are unusually high ("mass extinctions") compared with background rates? Whitlock and Schluter (2009) give data on the number of extinctions of marine invertebrate families in 76 blocks of time of similar duration.

0 extinctions happened in none of the blocks

1 extinction happened in 13 blocks

2 extinctions happened in 15 blocks

3 extinctions happened in 16 blocks

4 extinctions happened in 7 blocks

5 extinctions happened in 10 blocks

6 extinctions happened in 4 blocks

7 extinctions happened in 2 blocks

8 extinctions happened in 1 block

9 extinctions happened in 2 blocks

"10 or more" extinctions happened in 6 blocks

Estimate the expected number of extinctions per block given the data above and compare the proportion of blocks predicted by the model for each of the above extinction numbers with the observed ones. Is there much difference between the two? Conduct the Chi-quare test (Calculate the Chi-square statistics and compare with the probability). Use the following app to calculate the probability that the chi-square of 9 degrees of freedom is larger than what you obtain. If that probability is less than 0.05 we will say that the Poisson model does not generate these data.