A marine biologist monitors a population of Great White Sharks, collecting data on the total length, LLL meters, and the body mass, MMM tonnes, of 12 specimen sharks. The data is summarised as follows:
SLL=19.4S_{LL} = 19.4SLL=19.4 ∑M2=69.67\sum M^2 = 69.67∑M2=69.67 ∑LM=123.46\sum LM = 123.46∑LM=123.46 ∑L=50.4\sum L = 50.4∑L=50.4 ∑M=25.8\sum M = 25.8∑M=25.8
Calculate the value of SLMS_{LM}SLM and the value of SMMS_{MM}SMM.
Calculate the value of the product moment correlation coefficient (PMCC) between LLL and MMM.
Show that the equation of the regression line of MMM on LLL can be written as
M=−1.12+0.778L M = -1.12 + 0.778L M=−1.12+0.778L(Rounding constants to 3 significant figures).
Give an interpretation of the gradient of the regression line.
Explain why it would not be appropriate to use this regression line to estimate the mass of a shark with a total length of 1.2 meters.
The biologist decides to code the data using u=L−2u = L - 2u=L−2 and v=5M+3v = 5M + 3v=5M+3.
Write down the value of the PMCC between uuu and vvv.
Write down an equation of the regression line of vvv on uuu. You do not need to simplify your equation.
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.