A machine is designed to fill bags of sugar with a target mean weight of 500 g. The weight of sugar in a bag is normally distributed. A quality control manager suspects the machine is underfilling the bags. The weights, xxx g, of 10 randomly selected bags are recorded, and the following statistics are calculated:
xˉ=492.5s=9.24 \bar{x} = 492.5 \quad s = 9.24 xˉ=492.5s=9.24Stating your hypotheses clearly, test at the 5% significance level whether or not the manager's suspicion is supported.
130 exam-style questions on Edexcel A Level Maths 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.