A marine biologist is investigating the attenuation of light in a high-altitude freshwater lake. She hypothesizes that the light intensity decreases as the depth from the surface increases. She records the depth below the surface, xxx meters, and the light intensity, LLL lux, at seven different points. The data collected is shown in the table below:
Depth x (m)2.56.010.516.022.530.040.0Intensity L (lux)580420450280190230110\begin{array}{|l|c|c|c|c|c|c|c|} \hline \text{Depth } x \text{ (m)} & 2.5 & 6.0 & 10.5 & 16.0 & 22.5 & 30.0 & 40.0 \\ \hline \text{Intensity } L \text{ (lux)} & 580 & 420 & 450 & 280 & 190 & 230 & 110 \\ \hline \end{array}Depth x (m)Intensity L (lux)2.55806.042010.545016.028022.519030.023040.0110Calculate Spearman's rank correlation coefficient for these data.
Stating your hypotheses clearly, test at the 5% level of significance whether or not the data provides support for the biologist's hypothesis that light intensity decreases as depth increases.
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.