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.
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.