For a random sample of 40 cars, the correlation coefficient between a car's mass and its CO2 _2\,2 emission is 0.31.
For n=40n = 40n=40, the critical value for a one-tailed test at the 5% significance level for the population correlation coefficient is 0.2638, and the critical value for a two-tailed test at the 5% significance level is 0.3120.
A researcher tests, at the 5% significance level, whether there is positive correlation between mass and CO2 _2\,2 emission in the population. State the conclusion of this test, with a reason.
A second researcher tests, at the 5% significance level, whether there is any correlation between the two variables in the population. State the conclusion of this test, with a reason.
Explain how the same value of 0.31 can lead to these two different conclusions.
157 exam-style questions on AQA A Level Maths 2.2.2 Scatter diagrams and correlation. Each one has a worked solution and a mark scheme showing where the marks go.