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.
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.