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.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.