Find the variance and the mean of the number of arrests per cell, and use the variance- mean ratio to test the hypothesis that the arrests are distributed randomly over the area (against the two-tailed hypothesis that they are not).

The police have made arrests at the following locations:

First we find the mean number of points per cell. There are 35 cells and 22 points, so that xmean

= 22 / 35 = 0.629.

Next we find the variance of the number of points per cell:



Next we calculate the VMR:

VMR = s2

/ xmean = 0.299 / 0.629 = 0.476

Finally, we find the z value:

z = sqrt((m - 1) /2) (VMR - 1)

z = sqrt((35 - 1) /2) (0.476 - 1) = -2.161

With alpha equal to 0.05, the critical values are -1.96 and +1.96. The z-score is less than

the critical value, so that we reject the null hypothesis of no pattern. The data imply spatial

dispersion.