A random sample of 40 oak trees was studied by a biologist. She recorded the height hhh in meters and the trunk diameter ddd in centimeters of each tree.
The following summary statistics were calculated from these data:
∑h=680,∑h2=11776,∑d=1440,∑hd=25012,Sdd=2240 \sum h = 680, \quad \sum h^2 = 11776, \quad \sum d = 1440, \quad \sum hd = 25012, \quad S_{dd} = 2240 ∑h=680,∑h2=11776,∑d=1440,∑hd=25012,Sdd=2240Find ShhS_{hh}Shh and ShdS_{hd}Shd.
Calculate, to 3 significant figures, the product moment correlation coefficient between hhh and ddd.
Give an interpretation of your coefficient in the context of the biologist's study.
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.