A marine biologist investigates the relationship between the concentration of a specific micro-plastic (xxx, measured in particles per litre) and the reproductive rate of a plankton colony (yyy, measured in offspring per individual). For a random sample of 25 water stations, the product moment correlation coefficient was calculated as r=−0.491r = -0.491r=−0.491. The data is assumed to be drawn from a bivariate normal distribution. Carry out a hypothesis test at the 1% significance level to determine whether there is evidence of a negative correlation between micro-plastic concentration and plankton reproduction. The critical value for the product moment correlation coefficient at the 1% significance level for a sample size of 25 is 0.4622.
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.