A chemical manufacturing plant monitors the dynamic viscosity of a specialized polymer. Historical records indicate that the viscosity follows a normal distribution with a mean of 214.5 centipoise214.5\text{ centipoise}214.5 centipoise and a standard deviation of 18.4 centipoise18.4\text{ centipoise}18.4 centipoise.
After modifying the cooling stage of the production process, it is suggested that the mean viscosity of the polymer has changed. To investigate this claim, a random sample of 40 batches is tested under the new conditions.
The sum of the viscosity measurements for these 40 batches is found to be 8825.2 centipoise8825.2\text{ centipoise}8825.2 centipoise.
Assuming that the viscosity values remain normally distributed, test at the 5% significance level the claim that the mean viscosity has changed.
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.