James runs a fish and chip shop. He records the mean daily temperature, t ∘Ct\,^{\circ}\text{C}t∘C, and the daily sales, £S\pounds S£S, on each of 10 randomly chosen days in the summer.
The product moment correlation coefficient between t t\,t and S S\,S for these data is 0.67.
For n=10n = 10n=10, the critical value for a one-tailed test at the 5% level for the population correlation coefficient is 0.5494.
Carry out a hypothesis test at the 5% significance level to determine whether there is a positive correlation between daily sales and mean daily temperature.
James suggests that a linear regression model could be used for these data. State, giving a reason, whether the value of the correlation coefficient is consistent with James's suggestion.
State, giving a reason, which of the two variables is the explanatory variable.
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.