The distance of a cargo vessel from a submerged hydrophone, LLL km, and the detected underwater noise level, DDD dB, were recorded on 12 separate occasions. The collected data are summarised as follows:
SLL=225 S_{LL} = 225 SLL=225 ∑D=840 \sum D = 840 ∑D=840 ∑D2=60 800 \sum D^2 = 60\,800 ∑D2=60800 SLD=−540 S_{LD} = -540 SLD=−540Find the value of SDDS_{DD}SDD.
Calculate, to 3 significant figures, the product moment correlation coefficient for these data.
Give an interpretation of your coefficient in context.
An engineer decides to use the variable MMM to represent the distance from the hydrophone in metres, such that M=1000LM = 1000LM=1000L.
Write down the value of SMMS_{MM}SMM.
Write down the value of the product moment correlation coefficient between MMM and 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.