A biologist will test, using a random sample of 20 pairs of observations, whether two variables are correlated in a population whose correlation coefficient is $ρ\rho$ .

For $n = 20$ , the critical value for a one-tailed test for the population correlation coefficient is 0.3783 at the 5% level and 0.4438 at the 2.5% level.

The biologist tests, at the 5% significance level, whether there is any correlation between the two variables. Find, in set notation, the set of values of the sample correlation coefficient $r\,$ for which the null hypothesis would be rejected.

The biologist instead tests, at the 5% significance level, whether there is positive correlation between the two variables. Find, in set notation, the set of values of $r\,$ for which the null hypothesis would be rejected, and state, giving a reason, whether this test is more or less likely than the test in part (a) to reject the null hypothesis when $\rho\,$ is positive.

A biologist will test, using a random sample of 20 pairs of observations, whether two variables are correlated in a population whose correlation coefficient is $ρ\rho$ .

For $n = 20$ , the critical value for a one-tailed test for the population correlation coefficient is 0.3783 at the 5% level and 0.4438 at the 2.5% level.

2.2.2 Scatter diagrams and correlation

Question 14

Markscheme

2.2.2 Scatter diagrams and correlation

Question 14

Markscheme

2.2.2 Scatter diagrams and correlation

Question 14

2.2.2 Scatter diagrams and correlation Questions

2.2.2 Scatter diagrams and correlation

Question 14

2.2.2 Scatter diagrams and correlation Questions