Two-tailed Test

A food manufacturer produces thousands of packets of flour each day. The mass of flour in a packet follows a normal distribution with mean \(505\) g and standard deviation \(0.8\) g.

Following a slight adjustment to the filling machine, the mass, \(x\) g, of the flour in \(12\) randomly chosen packets is summarised by

\(\sum x = 6063.5\), \(\sum x^{2} = 3063841.81\)

Assuming that the variance of the distribution is unaltered by the adjustment, test at the \(5\%\) significance level whether there is any change in the mean mass of the flour.