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.
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.