The flight time of a specific model of commercial drone is assumed to follow a normal distribution with mean μ \mu\,μ minutes and standard deviation σ \sigma\,σ minutes. A reliability engineer selects a random sample of 12 drones and records their flight times until battery depletion. The resulting data yields an unbiased estimate of the mean tˉ=42.8\bar{t} = 42.8tˉ=42.8 minutes and an unbiased estimate of the variance s2=14.4s^2 = 14.4s2=14.4 minutes2^22.
Test, at the 5% significance level, whether there is evidence that the standard deviation of flight times, σ\sigmaσ, is greater than 3.0 minutes. State your hypotheses clearly.
Test, at the 5% significance level, whether there is evidence that the population mean flight time, μ\muμ, is greater than 40.0 minutes.
State a necessary assumption regarding the distribution of flight times for these tests to be valid.
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.