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.
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.