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.
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.