A conservation scientist records nitrate concentration c c\,c mg L−1^{-1}−1 and a plant-diversity index d d\,d at randomly selected river sites. The correlation coefficient is -0.760, with a one-tailed p-value of 0.006. The regression line fitted for 5≤c≤40 5\leq c\leq40\,5≤c≤40 is d=8.4−0.12cd=8.4-0.12cd=8.4−0.12c.
Test at the 1% significance level whether there is evidence of negative association.
Interpret the gradient of the regression line.
Estimate the diversity index at a site with nitrate concentration 30 mg L−1^{-1}−1.
Explain why the test does not establish that nitrate concentration causes the change in diversity.
Explain why the model should not be used to predict the index when c=70c=70c=70.
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.