A chemical engineer is studying the effect of a specific catalyst concentration, CCC (mol/L), on the rate of gas production, RRR (mL/s). The data for 8 experimental trials are recorded in the table below:
Trial12345678Concentration (C)0.050.120.180.250.320.440.580.75Rate (R)1.42.94.23.86.55.99.18.2\begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \text{Trial} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \text{Concentration } (C) & 0.05 & 0.12 & 0.18 & 0.25 & 0.32 & 0.44 & 0.58 & 0.75 \\ \hline \text{Rate } (R) & 1.4 & 2.9 & 4.2 & 3.8 & 6.5 & 5.9 & 9.1 & 8.2 \\ \hline \end{array}TrialConcentration (C)Rate (R)10.051.420.122.930.184.240.253.850.326.560.445.970.589.180.758.2
Calculate Spearman’s rank correlation coefficient between catalyst concentration and production rate, giving your answer to 3 decimal places.
Test, at the 5% significance level, whether there is evidence of a positive correlation between catalyst concentration and production rate. State your hypotheses clearly.
A junior researcher suggests that the product moment correlation coefficient (PMCC) should be used instead. The PMCC for this specific data set is calculated to be 0.924 (to 3 decimal places).
Use this PMCC value to test for evidence of a positive linear correlation at the 5% significance level.
Comparing your results from parts (b) and (c), explain what the relative values of these coefficients suggest about the relationship between catalyst concentration and gas production rate.
340 exam-style questions on Edexcel A Level Maths Regression, Correlation and Hypothesis Testing, covering 1.1 Exponential Models, 1.2 Measuring Correlation, and 1.3 Hypothesis Testing for Zero Correlation. Each one has a worked solution and a mark scheme showing where the marks go.