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.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.