Testing for zero correlationEdexcel A-Level Further Maths: Mind map

Exam questions on Testing for zero correlation

1. For a random sample of 10 adults, the product moment correlation coefficient between weekly hours of exercise and resting heart rate is $r=-0.60$. A test is to be carried out, at the 5% significance level, to see whether there is any correlation between the two variables in the population.
   The researcher now only wants to test for negative correlation, using $H_0:\rho=0$ and $H_1:\rho<0$ at the 5% significance level. Using the critical value $-0.5494$, carry out the test and state your conclusion in context.2 marks
2. A teacher ranks 8 students by their coursework mark and by their end-of-year examination mark. Spearman's rank correlation coefficient between the two sets of ranks is $r_s=0.69$. The teacher tests, at the 5% significance level, whether there is positive correlation between coursework and examination performance.
   Using the critical value $0.6429$, complete the test and state your conclusion in context.2 marks
3. A farmer applies different masses of fertiliser to 12 randomly chosen plots of land. The product moment correlation coefficient between the mass of fertiliser and the crop yield is $r=0.65$.
   Test, at the 5% significance level, whether there is positive correlation between the mass of fertiliser and the crop yield. Use the critical value $0.4973$ and state the hypotheses clearly.3 marks