A microbiologist studying hospital surfaces finds that a specific strain of bacteria naturally occurs at a mean rate of 120 colonies per square metre. A Poisson distribution is used to model the number of colonies in any sampled area.
A sample area of 0.05 m2 is selected at random. Determine the critical region for a two-tailed test to investigate whether the mean rate of colonisation has changed from the known average. Use a 10% level of significance, ensuring the probability of rejection in each tail is less than 0.05.
Calculate the actual significance level of the test defined in part (a).
The hospital implements a new high-intensity ultraviolet cleaning protocol. The microbiologist claims that this protocol significantly reduces the mean bacterial rate.
A large-scale inspection is conducted on a floor area of 2.5 m2, and a total of 275 colonies are detected.
Using a suitable approximation, test the microbiologist's claim at a 5% level of significance. You should state your hypotheses clearly.
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.