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.
278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.