N2017 P2 Q7

The production manager of a food manufacturing company wishes to take a random sample of a certain type of biscuit bar from the thousands produced one day at his factory, for quality control purposes. He wishes to check that the mean mass of the bars is \(32\) grams, as stated on the packets.

1. State what it means for a sample to be random in this context.[1]

The masses, \(x\) grams, of a random sample of \(40\) biscuit bars are summarised as follows.

\[n=40\qquad\sum(x-32)=-7.7\qquad\sum(x-32)^2=11.05\]

2. Calculate unbiased estimates of the population mean and variance of the mass of biscuit bars.[2]
3. Test, at the \(1\%\) level of significance, the claim that the mean mass of biscuit bars is \(32\) grams. You should state your hypotheses and define any symbols you use.[5]
4. Explain why there is no need for the production manager to know anything about the population distribution of the masses of the biscuit bars.[2]