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.
278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.