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.
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.