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.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.