A marine biologist investigates the relationship between the depth of water, ddd (in metres), and the concentration of dissolved oxygen, ccc (in mg/L), at 12 specific locations in a deep-sea trench. The following summary statistics were recorded from the collected data:
Sdd=840.5Scc=15.2Sdc=−102.4 S_{dd} = 840.5 \quad S_{cc} = 15.2 \quad S_{dc} = -102.4 Sdd=840.5Scc=15.2Sdc=−102.4Calculate the product moment correlation coefficient (PMCC) for this set of data.
Interpret the calculated PMCC value within the context of the marine biologist's investigation.
The biologist later decides to convert the depth measurements from metres to centimetres by multiplying each ddd value by 100 and then adding a constant sensor offset of 5. Write down the value of the PMCC that would be obtained using these coded depth values and the original concentration values.
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.