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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.