An ornithologist models wingbeat frequency f f\,f in beats per minute using body mass m m\,m grams. The correlation coefficient between m m\,m and f f\,f is -0.878, while that between lnm \ln m\,lnm and lnf \ln f\,lnf is -0.992. The fitted regression line is lnf=4.70−0.330lnm\ln f=4.70-0.330\ln mlnf=4.70−0.330lnm.
Explain why a power model is preferable to a linear model for these data.
Find the power model for f f\,f in terms of mmm, giving the multiplicative constant to 3 significant figures.
Use the model to estimate f f\,f when m=25m=25m=25.
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.