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.
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.