A researcher is studying the relationship between the daily average temperature, ttt in ∘C^{\circ}\text{C}∘C, and the daily electricity consumption, eee in megawatt-hours (MWh), for a small town. A random sample of 10 days is taken and the results are recorded.
The data are summarised as follows:
n=10,∑t=184,∑e=412,∑e2=17540,Stt=226.4,Ste=−198.8 n = 10, \quad \sum t = 184, \quad \sum e = 412, \quad \sum e^2 = 17540, \quad S_{tt} = 226.4, \quad S_{te} = -198.8 n=10,∑t=184,∑e=412,∑e2=17540,Stt=226.4,Ste=−198.8Calculate the product moment correlation coefficient between ttt and eee.
Give an interpretation of your product moment correlation coefficient in the context of the study.
Find the equation of the least squares regression line of eee on ttt in the form e=a+bte = a + bte=a+bt.
Give an interpretation of the value of bbb in your regression line.
(i) Use the regression line from part (c) to estimate the electricity consumption for a day with an average temperature of 25∘C25^{\circ}\text{C}25∘C.
(ii) Comment on the reliability of your answer in part (i) given that the range of temperatures in the sample was 12∘C12^{\circ}\text{C}12∘C to 22∘C22^{\circ}\text{C}22∘C.
Using the regression line from part (c), the researcher estimates that for a temperature decrease of x ∘Cx \, ^{\circ}\text{C}x∘C there will be an increase of 555 MWh in electricity consumption.
Find the value of xxx.
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.