A marine biologist suspects that the mean length of a specific species of deep-sea eel has changed from its historical value of 85 cm due to rising ocean temperatures. She collects a random sample of 12 eels and measures their lengths, recording the following data in cm:
89.2,87.5,91.0,86.4,88.8,90.1,87.9,89.5,88.2,86.7,89.3,87.4 89.2, \quad 87.5, \quad 91.0, \quad 86.4, \quad 88.8, \quad 90.1, \quad 87.9, \quad 89.5, \quad 88.2, \quad 86.7, \quad 89.3, \quad 87.4 89.2,87.5,91.0,86.4,88.8,90.1,87.9,89.5,88.2,86.7,89.3,87.4Assuming that the lengths of these eels are normally distributed with a standard deviation of 4.5 cm, perform a hypothesis test at the 2% significance level to determine if the mean length has changed.
130 exam-style questions on WJEC A Level Maths 4.3.2 Statistical hypothesis testing (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.