Chris is investigating the relationship between the length of time an employee has worked at his company, x x\,x years, and the time it takes that employee to complete a particular task, y y\,y hours.
Chris records the time taken by a random sample of 12 employees. The product moment correlation coefficient between x x\,x and y y\,y for this sample is -0.47.
For n=12n = 12n=12, the critical value for a one-tailed test at the 5% level for the population correlation coefficient is 0.4973.
Carry out a hypothesis test at the 5% significance level to determine whether there is a negative correlation between the length of time an employee has worked at the company and the time taken to complete the task.
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.