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.
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.