A sports scientist believes that, for adult runners, there is a positive correlation between weekly training time and aerobic fitness score.
She collects data from a random sample of 50 adult runners. The product moment correlation coefficient between weekly training time and aerobic fitness score for this sample is 0.31.
For n=50n = 50n=50, the critical value for a one-tailed test at the 2.5% level for the population correlation coefficient is 0.2787.
Carry out a hypothesis test at the 2.5% significance level to determine whether this sample provides evidence to support the scientist's belief.