Dr. Aris, a materials engineer, is investigating the degradation of a new polymer composite. He believes that as the duration of exposure to UV radiation (measured in hours, hhh) increases, the fracture toughness of the composite (measured in MPam\text{MPa}\sqrt{\text{m}}MPam, KKK) decreases. He collects data from a random sample of 181818 specimens and calculates the product moment correlation coefficient (PMCC) between exposure time and fracture toughness to be r=−0.425r = -0.425r=−0.425.
Dr. Aris decides to test his hypothesis at the 5%5\%5% level of significance.
The table below shows the critical values for the PMCC for a sample size of 181818 for various significance levels.
1-tailed test significance level5%2.5%1%0.5%2-tailed test significance level10%5%2%1%Critical value0.4000.4680.5430.590\begin{array}{|c|c|c|c|c|} \hline \text{1-tailed test significance level} & 5\% & 2.5\% & 1\% & 0.5\% \\ \hline \text{2-tailed test significance level} & 10\% & 5\% & 2\% & 1\% \\ \hline \text{Critical value} & 0.400 & 0.468 & 0.543 & 0.590 \\ \hline \end{array}1-tailed test significance level2-tailed test significance levelCritical value5%10%0.4002.5%5%0.4681%2%0.5430.5%1%0.590Determine Dr. Aris's conclusion for his investigation, justifying your answer.
Practise Edexcel A Level Maths Regression, Correlation and Hypothesis Testing with exam-style questions for A Level Maths. 202 questions covering Exponential Models, Measuring Correlation, and Hypothesis Testing for Zero Correlation, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
