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.
130 exam-style questions on WJEC A Level Maths 4.3.2 Statistical hypothesis testing (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.