A fish-and-chip shop records mean daytime temperature ttt °C and daily sales S S\,S pounds on 10 randomly selected summer days. The correlation coefficient is 0.670, with a one-tailed p-value of 0.017. The regression line is S=5148+141tS=5148+141tS=5148+141t.
Test at the 5% significance level whether there is evidence of positive association.
Identify the explanatory variable and justify your choice.
Interpret the gradient.
Explain why the result does not prove that warmer weather causes higher sales.
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.