A factory manufactures steel rods with length L L\,L cm, where L∼N(μ,σ2)L \sim \mathrm{N}(\mu, \sigma^2)L∼N(μ,σ2). From a random sample of rods, an 80% confidence interval for μ \mu\,μ is calculated as (74.36,75.64)(74.36, 75.64)(74.36,75.64).
Find a 95% confidence interval for μ\muμ.
Using the formula for the volume of a rod V=10LV = 10LV=10L, find a 95% confidence interval for the mean volume of these rods.
If four independent random samples are taken and a 95% confidence interval for μ \mu\,μ is calculated for each, find the probability that at least three of these intervals will contain the true value of μ\muμ.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.