Under the Weights and Measures (Packaged Goods) Regulations 1986, display of the text '330 ml e' on a bottle of beer with nominal content volume of 330 ml means that not more than 2.5% of bottles may be deficient in content volume by more than the tolerable negative error (TNE) specified for the nominal quantity (Trading Standards Net). The TNE for nominal volume of 330 ml is 3% of the nominal volume. A brewery has bottling machines which deliver amounts that are normally distributed with known standard deviation 6 ml and which are capable of filling bottles with nominal capacities of both 330 and 500 ml. Explain why, when filling 330 ml bottles, the brewery should aim to set up the filling process to operate with a mean of 332 ml (to the nearest ml). Following set-up for a run of 330 ml bottles, after a run of 500 ml bottles, a sample of 24 bottles was checked and found to have the content volumes stored in Beer. xls. Use hypothesis testing to investigate whether or not the machine has been set up correctly.

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