The quality control department of a precision engineering firm monitors the manufacturing of high-tensile bolts. Historical data indicates that the mean length of the bolts is 145.0 mm145.0\text{ mm}145.0 mm with a standard deviation of 0.8 mm0.8\text{ mm}0.8 mm.
Following a recalibration of the cutting machines, a technician suspects that the mean length of the bolts has changed. To investigate this suspicion, a random sample of 256256256 bolts is measured.
The total length of these 256256256 bolts is found to be 37148.16 mm37148.16\text{ mm}37148.16 mm.
Assuming the lengths are normally distributed, test the technician's suspicion at the 5%5\%5% significance level.
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.