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.
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.