A road-safety researcher believes that, for cars of a given model, there is a negative correlation between the age of the car in years and its fuel economy in miles per gallon.
She collects data from a random sample of 30 cars of this model. The product moment correlation coefficient between age and fuel economy for this sample is -0.38.
For these data, the ppp-value for a one-tailed test of the population correlation coefficient is 0.019.
Carry out a hypothesis test at the 5% significance level to determine whether the sample supports the researcher's belief.
The researcher concludes that a car becoming older causes its fuel economy to fall. Explain why her data alone do not justify this conclusion.
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.