A football coach measures the height, h h\,h cm, and the weight, w w\,w kg, of each of a random sample of 12 players in a league.
The product moment correlation coefficient between h h\,h and w w\,w for this sample is 0.81, and the regression line of w w\,w on h h\,h for these data is
w=1.37h−173w = 1.37h - 173w=1.37h−173
For n=12n = 12n=12, the critical value for a one-tailed test for the population correlation coefficient is 0.4973 at the 5% level and 0.6581 at the 1% level.
Give an interpretation of the gradient of this regression line.
Carry out a hypothesis test at the 5% significance level to determine whether there is a positive correlation between the height and the weight of players in this league.
Determine whether the same conclusion would be reached at the 1% significance level.
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.