A scientist is studying the relationship between the concentration of a chemical catalyst, x x\,x units, and the time taken for a reaction to complete, y y\,y seconds.
The scientist records data for 20 different concentrations and finds the product moment correlation coefficient between concentration and reaction time to be -0.35.
Stating your hypotheses clearly and using a 5% level of significance, test whether or not there is evidence of a negative correlation between concentration and reaction time.
The scientist proposes a power model and codes the data using m=log10xm = \log_{10}xm=log10x and n=log10yn = \log_{10}yn=log10y. The regression line is n=2.45−0.72mn = 2.45 - 0.72mn=2.45−0.72m.
The product moment correlation coefficient for the coded data is found to be -0.92.
Explain how this value supports the scientist's proposal.
Show that the relationship between x x\,x and y y\,y can be written in the form y=axby = ax^by=axb where a a\,a and b b\,b are constants to be found.
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.