Marine biologists are investigating the relationship between the depth of a lake, DDD (metres), and the dissolved oxygen concentration, CCC (mg/L). For a sample of n=12n = 12n=12 measurements, the biologists code the data using the variables x=D−123x = \frac{D - 12}{3}x=3D−12 and y=C−50.5y = \frac{C - 5}{0.5}y=0.5C−5. The summary statistics for the coded data are as follows:
∑x=24Sxx=110∑y=48Syy=260∑xy=−12 \sum x = 24 \quad S_{xx} = 110 \quad \sum y = 48 \quad S_{yy} = 260 \quad \sum xy = -12 ∑x=24Sxx=110∑y=48Syy=260∑xy=−12Calculate the product-moment correlation coefficient between xxx and yyy. Give your answer to 3 decimal places.
Write down the value of the product-moment correlation coefficient for DDD and CCC.
A researcher suggests that deeper water contains lower levels of dissolved oxygen.
State, with a reason, whether or not the researcher's suggestion is supported by these data.
244 exam-style questions on AQA A Level Maths 2.2 L: Data presentation and interpretation, covering 2.2.1 Single-variable data diagrams, 2.2.2 Scatter diagrams and correlation, 2.2.3 Central tendency, variation and standard deviation, 2.2.4 Outliers and cleaning data, and 2.2 L: Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.