The flight times of a particular model of reconnaissance drone, T T\,T minutes, are normally distributed with an unknown mean μ \mu\,μ and a known standard deviation σ\sigmaσ. A random sample of 144 flights provided a 98% confidence interval for μ \mu\,μ of (45.837,48.163)(45.837, 48.163)(45.837,48.163).
Without carrying out any further calculations, use this confidence interval to test whether or not μ=48.5\mu = 48.5μ=48.5. State your hypotheses clearly and write down the significance level you have used.
A second study of 200 flights recorded a mean flight time of 46.2 minutes.
Determine a 90% confidence interval for μ \mu\,μ based on this second study.
162 exam-style questions on AQA A Level Maths 2.5 O: Statistical hypothesis testing, covering 2.5.1 Language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, and 2.5.3 Hypothesis test for a Normal mean (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.