8 The amounts spent on the weekly food shopping by families in the big city \(P\) and the small town \(Q\) are to be compared. The amounts spent, in dollars, in \(P\) and \(Q\) are denoted by \(x\) and \(y\) respectively. For a random sample of 60 families in \(P\) and a random sample of 50 families in \(Q\), the amounts are summarised as follows. $$\Sigma x = 9600 \quad \Sigma x ^ { 2 } = 1560000 \quad \Sigma y = 7200 \quad \Sigma y ^ { 2 } = 1052500$$ Assuming a common population variance, find

1. a pooled estimate for the population variance,
2. a \(95 \%\) confidence interval for the difference in the population means in \(P\) and \(Q\).