6 Alex obtained the actual waist measurements, \(w\) inches, of a random sample of 50 pairs of jeans, each of which was labelled as having a 32 -inch waist. The results are summarised by $$n = 50 , \quad \Sigma w = 1615.0 , \quad \Sigma w ^ { 2 } = 52214.50$$ Test, at the \(0.1 \%\) significance level, whether this sample provides evidence that the mean waist measurement of jeans labelled as having 32 -inch waists is in fact greater than 32 inches. State your hypotheses clearly. \section*{Jan 2006}