James runs a fish and chip shop. He records the average daily temperature, t∘Ct^{\circ}\text{C}t∘C, and the daily sales, £S\pounds S£S, for 10 days in the summer. The product moment correlation for these data is 0.67
Stating your hypotheses clearly and using a 5% significance level, test whether there is a positive correlation between daily sales and daily temperature.
James suggests that a linear regression model could be used to model the data.
State, giving a reason, whether or not the correlation coefficient is consistent with James's suggestion.
State, giving a reason, which variable would be the explanatory variable.
James calculated the linear regression equation as S=5148+141tS = 5148 + 141tS=5148+141t
Give an interpretation of the gradient of this regression equation.
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.