An environmental scientist studied the relationship between the daily average temperature, xxx (in ∘C^{\circ}\text{C}∘C), and the daily electricity consumption, yyy (in MWh), for a small town over 15 days in summer. The following summary statistics were calculated:
Sxx=450.4Syy=1240.2Sxy=652.8 S_{xx} = 450.4 \quad S_{yy} = 1240.2 \quad S_{xy} = 652.8 Sxx=450.4Syy=1240.2Sxy=652.8Calculate the product moment correlation coefficient (PMCC) for these data.
Interpret the value of the PMCC in the context of the study.
A student later coded the data by multiplying the temperature figures by 1.8 and adding 32 (to convert to Fahrenheit). Write down the value of the PMCC calculated using the coded data.
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.