A researcher is investigating the relationship between the distance from a sound source, x x\,x metres, and the measured intensity of the sound, y y\,y units.
The researcher measures 15 different distances and finds the product moment correlation coefficient between distance and sound intensity to be -0.48.
Using a 5% level of significance, test whether or not there is evidence of a negative correlation between distance and sound intensity. State your hypotheses clearly.
The researcher codes the data using m=log10xm = \log_{10}xm=log10x and n=log10yn = \log_{10}yn=log10y and obtains the model n=3.62−1.95mn = 3.62 - 1.95mn=3.62−1.95m.
The product moment correlation coefficient for the coded data is -0.98.
Explain why this supports the researcher's choice of a non-linear model.
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.
104 exam-style questions on WJEC A Level Maths 1.6 Exponentials and logarithms, covering 1.6.1 Exponentials and logarithms, 1.6.2 Exponentials and logarithms, 1.6.3 Exponentials and logarithms, 1.6.4 Exponentials and logarithms, 1.6.5 Exponentials and logarithms, 1.6.6 Exponentials and logarithms, 1.6.7 Exponentials and logarithms, 1.6.8 Exponentials and logarithms, and 1.6.9 Exponentials and logarithms. Each one has a worked solution and a mark scheme showing where the marks go.