State two conditions under which it might be more appropriate to use Spearman’s rank correlation coefficient rather than the product moment correlation coefficient.
A researcher took a random sample of 12 luxury watches from a boutique. The price, in pounds, and the age, in years, of each watch were recorded.
The Spearman’s rank correlation coefficient between the results was calculated as rs=−0.598r_s = -0.598rs=−0.598.
Test, at the 5% level of significance, whether or not there is evidence of a correlation. State clearly your hypotheses and the critical value used.
The product moment correlation coefficient (PMCC) between the results was calculated as r=−0.482r = -0.482r=−0.482.
Test, at the 5% level of significance, whether or not there is evidence of a negative correlation. State clearly your hypotheses and the critical value used.
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.