Dilan is investigating whether two variables are correlated in a population whose correlation coefficient is ρ\rhoρ. He takes a random sample of 25 pairs of observations and obtains a product moment correlation coefficient of -0.42.
For n=25n = 25n=25, the critical value for a one-tailed test for the population correlation coefficient is 0.3365 at the 5% level and 0.3961 at the 2.5% level.
Dilan writes the following.
H0:r=0H_0: r = 0H0:r=0, H1:r>0H_1: r > 0H1:r>0 −0.42<0.3365-0.42 < 0.3365−0.42<0.3365, so accept H0H_0H0. There is no correlation between the two variables.
Identify four errors in Dilan's work.
Dilan's supervisor tells him that he should have tested, at the 5% significance level, for any correlation between the two variables. Carry out that test correctly.
244 exam-style questions on AQA A Level Maths 2.2 L: Data presentation and interpretation, covering 2.2.1 Single-variable data diagrams, 2.2.2 Scatter diagrams and correlation, 2.2.3 Central tendency, variation and standard deviation, 2.2.4 Outliers and cleaning data, and 2.2 L: Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.