An environmental study measures the nitrogen concentration, xxx mg/L, and the dissolved oxygen level, yyy mg/L, at 15 different sites along an industrial canal. The data are summarised as follows:
Sxx=2 400S_{xx} = 2\,400Sxx=2400 ∑y=1 020\sum y = 1\,020∑y=1020 ∑y2=72 400\sum y^2 = 72\,400∑y2=72400 Sxy=−1 950S_{xy} = -1\,950Sxy=−1950
Determine the value of SyyS_{yy}Syy.
Calculate the product moment correlation coefficient for these data, giving your answer to 3 significant figures.
Interpret the value of the correlation coefficient in the context of the study.
A scientist converts the nitrogen concentration into grams per litre, www, such that w=x1000w = \frac{x}{1000}w=1000x.
State the value of SwwS_{ww}Sww.
State the value of the product moment correlation coefficient between www and yyy.
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.