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.
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.