A chemical engineer is studying the relationship between the concentration of a new catalyst, ccc grams per litre, and the time taken for a specific polymerization reaction to complete, ttt minutes. The engineer suspects that there is a negative correlation between the catalyst concentration and the reaction time.
A random sample of 60 trials is conducted. The product moment correlation coefficient (PMCC) for this sample is calculated as r=−0.312r = -0.312r=−0.312.
Carry out a hypothesis test at the 1% significance level to determine if the sample provides sufficient evidence to support the engineer's suspicion.
For n=60n = 60n=60, the critical value for a one-tailed test at the 1% level for the population correlation coefficient is 0.2997.
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.