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.
202 exam-style questions on Edexcel A Level Maths Regression, Correlation and Hypothesis Testing, covering 1.1 Exponential Models, 1.2 Measuring Correlation, and 1.3 Hypothesis Testing for Zero Correlation. Each one has a worked solution and a mark scheme showing where the marks go.