The age and education distributions are given in Graph 1 . Both graphs show large differences between the county-wide data and the jury data. The question is how strong these differences statistically are. In order to answer this question we use the chi-square statistic given by chi-square=(observed frequency - expected frequency)^2/(expected frequency).

The observed and expected frequencies for the age distribution are given in the following Table:

Age Observed Expected------------------------------------------------ 21-40 5 27.7 41-50 9 15.2 51-60 19 10.6 > 61 33 12.5

The chi-square statistic is equal to 61 with 3 degrees of freedom and an approximate p-value of zero. This implies that with simple random sampling, it is almost impossible for a jury to differ this much from the county age distribution (thus confirming the visual result of the first graph).

Similarly, for the education distribution the chi-square=152.5, with 3 degrees of freedom and an approximate p-value of zero. With respect to education the result is even more extreme.

From these two tests we can conclude that the age and education characteristics of the selected jurors in Alameda County do not follow the demographic patterns of the population of the county. The reason is, as the journal notices, that grand juries are nominated by judges who showed a clear preference to older and more educated jurors.