An industrial packaging plant produces bags of 'Premium Blend' coffee. Historically, the mass of coffee in a bag, MMM grams, followed a normal distribution with a mean of 505 g505 \text{ g}505 g and a standard deviation of 12 g12 \text{ g}12 g.
A quality control manager decides to investigate the calibration of the machines. On a Monday morning, she records the mass of the first 808080 bags produced by Machine A.
(i) Identify the sampling method used to collect these data.
(ii) Explain why this specific sample may not be appropriate for a formal hypothesis test regarding the entire production line.
Following a suspected technical fault, a second independent sample of 808080 bags is selected using a simple random sampling method. The mean mass of this sample is found to be 501.5 g501.5 \text{ g}501.5 g.
Using a 1%1\%1% significance level, test whether there is evidence that the mean mass of the coffee bags has decreased.
You should assume that the mass of coffee bags remains normally distributed and the standard deviation is unchanged at 12 g12 \text{ g}12 g.
162 exam-style questions on AQA A Level Maths 2.5 O: Statistical hypothesis testing, covering 2.5.1 Language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, and 2.5.3 Hypothesis test for a Normal mean (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.