5. A shopkeeper sells chocolate bars which are described by the manufacturer as having an average mass of 45 grams. The shopkeeper claims that the mass of the chocolate bars, \(X\) grams, is getting smaller on average. A random sample of 6 chocolate bars is taken and their masses in grams are measured. The results are $$\sum x = 246 \quad \text { and } \quad \sum x ^ { 2 } = 10198$$ Investigate the shopkeeper's claim using the \(5 \%\) level of significance.
State any assumptions that you make.
[0pt] [9 marks]