A cereal manufacturer produces packets of ‘own-brand’ muesli for a supermarket chain using the same production line as they use for their own premium brand. The mean and standard deviation of the oat content by weight of a random sample of 14 ‘own-brand’

packets are 34.9 per cent and 1.4 per cent. The mean and standard deviation of the oat content of a random sample of 17 premium brand packets are 33.4 per cent and 1.1 per cent.

Test the hypothesis that the mean oat content of the premium brand is no greater than the mean oat content of the ‘own-brand’ muesli using a 1 per cent level of significance. Oat content is Normally distributed in both brands.