A marine biologist measured the dissolved oxygen level, ddd mg/L, at various depths, hhh meters, in a specific estuary. Data from a random sample of 10 locations are summarized as follows:
∑h=155∑h2=2875∑d=62.4Sdd=18.2∑hd=884.2 \sum h = 155 \quad \sum h^2 = 2875 \quad \sum d = 62.4 \quad S_{dd} = 18.2 \quad \sum hd = 884.2 ∑h=155∑h2=2875∑d=62.4Sdd=18.2∑hd=884.2Calculate the values of ShhS_{hh}Shh and ShdS_{hd}Shd.
Calculate, to 3 significant figures, the product moment correlation coefficient between hhh and ddd.
The biologist also measured the water temperature, ttt °C, at the same 10 locations. The product moment correlation coefficient between hhh and ttt was found to be −0.915-0.915−0.915.
Describe, giving a reason, the nature of the correlation you would expect to find between temperature (ttt) and dissolved oxygen (ddd).
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.