A marine biologist is researching the relationship between the depth of a coral reef, ddd meters, and the number of distinct species, sss, identified at that depth. For a sample of n=12n = 12n=12 sites, the data is transformed using the coded variables u=d−1005u = \frac{d - 100}{5}u=5d−100 and v=s−204v = \frac{s - 20}{4}v=4s−20. The following summary statistics are recorded:
∑u=72Suu=150∑v=120Svv=600∑uv=505 \sum u = 72 \quad S_{uu} = 150 \quad \sum v = 120 \quad S_{vv} = 600 \quad \sum uv = 505 ∑u=72Suu=150∑v=120Svv=600∑uv=505Calculate the product-moment correlation coefficient for the coded variables uuu and vvv. Give your answer to 3 decimal places.
State the value of the product-moment correlation coefficient for the original variables ddd and sss.
The biologist suggests that deeper reef sites are likely to host a higher number of distinct species. Determine, with a reason, whether this suggestion is supported by the data.
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.