A manufacturer of high-precision capacitors specifies that the mean capacitance of a specific model is 14.50 μF14.50\, \mu \text{F}14.50μF. A quality control engineer believes that a recent manufacturing fault has resulted in a lower mean capacitance than specified. A random sample of 81 capacitors is tested, yielding a sample mean of 14.38 μF14.38\, \mu \text{F}14.38μF and a standard deviation of 0.45 μF0.45\, \mu \text{F}0.45μF. Test the engineer's belief at the 1% level of significance. State your hypotheses clearly.
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.