The data frame Cases. of .flu contains a list of cases of flu recorded in 3 London hospitals during each month of 2017 . Consider the following $R$ code and its output.

table (Cases. of.flu)

Month Hospital

$\begin{array}{lrrr}\text { Month } & \text { A } & \text { B } & \text { C } \\ \text { April } & 10 & 40 & 27\end{array}$

$\begin{array}{lrrr}\text { April } & 10 & 40 & 27 \\ \text { August } & 9 & 34 & 19\end{array}$

$\begin{array}{lrrr}\text { August } & 9 & 34 & 19 \\ \text { December } & 24 & 129 & 81\end{array}$

$\begin{array}{llll}\text { December } & 24 & 129 & 81 \\ \text { February } & 49 & 134 & 74\end{array}$

$\begin{array}{llll}\text { February } & 49 & 134 & 74 \\ \text { January } & 45 & 138 & 78\end{array}$

$\begin{array}{lrrr}\text { July } & 5 & 138 & 78 \\ & 11 & 36 & 35\end{array}$

$\begin{array}{llll}\text { June } & 11 & 36 & 22\end{array}$

$\begin{array}{llll}\text { March } & 20 & 82 & 41\end{array}$

May $5 \quad 43 \quad 23$

November $17 \quad 82 \quad 62$

October $6 \quad 26 \quad 19$

September $640 \quad 21$

Cases. of.flu.table = as.data.frame (table (Cases. of .flu))

$>$ head (Cases. of .flu.table)

Month Hospital Freq

1 April A 10

2 August A 9

3 December A 24

4 February A 49

5 January A 45

6 July A 5

$>\bmod 1=$ glm (Freq ., data=Cases. of .flu.table, family=poisson)

$>\bmod 1 \$ \mathrm{dev}$

[1] $28.51836$

levels (Cases. of.flu$Month)

Describe a test for the null hypothesis of independence between the variables Month and Hospital using the deviance statistic. State the assumptions of the test.

Perform the test at the $1 \%$ level for each of the two different models shown above. You may use the table below showing 99 th percentiles of the $\chi_{p}^{2}$ distribution with a range of degrees of freedom $p$. How would you explain the discrepancy between their conclusions?