Identify two conditions under which it would be more appropriate to use Spearman’s rank correlation coefficient rather than the product moment correlation coefficient (PMCC) to analyze the relationship between two variables.
A conservationist monitors the density of a rare orchid species, DDD (plants per m2m^2m2), and the local soil pH, ppp, across n=10n=10n=10 distinct plots in a meadow.
The Spearman’s rank correlation coefficient for the recorded data was found to be rs=0.655r_s = 0.655rs=0.655.
Investigate, at the 5% level of significance, whether there is statistical evidence of any correlation between the density of orchids and soil pH. Explicitly state your null and alternative hypotheses and the critical value used.
The product moment correlation coefficient (PMCC) for the same dataset was calculated as r=0.515r = 0.515r=0.515.
Determine, at the 5% level of significance, if there is evidence of a positive correlation between orchid density and soil pH. State your hypotheses clearly and include the relevant critical value.
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.