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.
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.