Under the Weights and Measures (Packaged Goods) Regulations
1986, display of the text ‘330 ml e’ on...

Question

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.

(i) 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). (ii) 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.

Rochak · Accepted Answer

i. The brewery should aim to set up the filling process to operate with a mean of 332 ml (to the nearest ml) to account for the standard deviation that arises due to the filling of the bottles
ii. Using the hypothesis testing, we can conclude that the machine has been set up correctly

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...

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