Exercise 7 - Defining Pollster Bias

The data do seem to suggest there is a difference between the pollsters. However, these data are subject to variability. Perhaps the differences we observe are due to chance. Under the urn model, both pollsters should have the same expected value: the election day difference, \(d\).

We will model the observed data \(Y_{ij}\) in the following way:

$$Y_{ij}=d+b_i+\varepsilon_{ij}$$

with \(i=1,2\) indexing the two pollsters, \(b_i\) the bias for pollster \(i\), and \(\varepsilon_{ij}\) poll to poll chance variability. We assume the \(\varepsilon\) are independent from each other, have expected value \(0\) and standard deviation \(\sigma_i\) regardless of \(j\).

Which of the following statements best reflects what we need to know to determine if our data fit the urn model?