The data does seem to suggest there is a difference. However, these data are subject to variability. Perhaps the differences we observe are due to chance. The urn model theory says nothing about...

The data does seem to suggest there is a difference. However, these data are subject to variability. Perhaps the differences we observe are due to chance. The urn model theory says nothing about pollster effect. Under the urn model, both pollsters have the same expected value: the election day difference, that we call d. To answer the question “is there an urn model?”, we will model the observed data Yi,j in the following way:

with i = 1, 2 indexing the two pollsters, bi the bias for pollster i and εij poll to poll chance variability. We assume the ε are independent from each other, have expected value 0 and standard deviation σi regardless of j.