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.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.