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.
121 exam-style questions on OCR A Level Maths 2.2 Data Presentation and Interpretation, covering 2.2.1 Tables and diagrams for single variable data, 2.2.2 Area in a histogram, 2.2.3 Scatter diagrams and regression lines, 2.2.4 Informal interpretation of correlation, 2.2.5 Correlation and causation, 2.2.6 Measures of average and spread, 2.2.7 Calculations of mean and standard deviation, 2.2.8 Outliers, 2.2.9 Selecting or critiquing data presentation, and 2.2.10 Cleaning data. Each one has a worked solution and a mark scheme showing where the marks go.