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.
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.