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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.