A biologist studying bacterial growth records the incubation time, ttt minutes, and the mass of nutrients consumed, mmm milligrams, for n=15n = 15n=15 separate samples. Each sample is initially provided with a petri dish containing 18.018.018.0 mg of nutrient. The summary statistics for these 151515 samples are as follows:
∑t=202.5,∑m=49.5,∑tm=745.2,Stt=1440.0,Smm=7.5 \sum t = 202.5, \quad \sum m = 49.5, \quad \sum tm = 745.2, \quad S_{tt} = 1440.0, \quad S_{mm} = 7.5 ∑t=202.5,∑m=49.5,∑tm=745.2,Stt=1440.0,Smm=7.5Calculate the product moment correlation coefficient between ttt and mmm.
The mass of nutrient remaining in the dish at the end of the incubation period is recorded as RRR milligrams. (i) Write down an equation for RRR in terms of mmm. (ii) State the value of the product moment correlation coefficient between RRR and mmm.
State the value of the product moment correlation coefficient between ttt and RRR.
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.