A chemical engineer is investigating the relationship between the reaction temperature TTT, in degrees Celsius, and the volume of byproduct VVV, in millilitres, produced in a specific industrial process. A sample of 50 reactions was monitored and the results were recorded.
The following summary statistics were calculated from these data:
∑T=1250,∑T2=32000,∑V=8000,∑TV=198400,SVV=4500 \sum T = 1250, \quad \sum T^2 = 32000, \quad \sum V = 8000, \quad \sum TV = 198400, \quad S_{VV} = 4500 ∑T=1250,∑T2=32000,∑V=8000,∑TV=198400,SVV=4500Find STTS_{TT}STT and STVS_{TV}STV.
Calculate, to 3 significant figures, the product moment correlation coefficient between TTT and VVV.
Give an interpretation of your coefficient in the context of the engineer's study.
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.