Worked Example 3

A beverage company produces thousands of cans of soda each day. The volume of a soda in a can follows a normal distribution with mean \(355\) ml and standard deviation \(1.2\) ml.

Following the maintenance of the filling machine, there may have been a slight adjustment. To determine if the machine still produces \(355\) ml of soda per can, \(15\) randomly chosen cans are chosen. The volume, \(x\) ml, of the \(15\) cans of soda is summarised by

\(\sum{x}=5314.5\), \(\sum{{{x}^{2}}=1892040.25}\)

Assuming that the variance of the distribution is unaltered by the adjustment, test at the \(6\%\) significance level whether there is any change in the mean volume of the soda.