A scientific robotic probe collects soil samples from a lunar crater. The mass M M\,M grams of each sample is modeled as a normal distribution M∼N(μ,σ2)M \sim \mathrm{N}(\mu, \sigma^2)M∼N(μ,σ2). Based on an initial batch of data, a 90% confidence interval for μ \mu\,μ is calculated as (122.35,127.65)(122.35, 127.65)(122.35,127.65).
Determine a 99% confidence interval for μ\muμ.
The total yield of a specific mineral extract from a sample is given by the linear transformation Y=20MY = 20MY=20M. Using your answer from part (a), find a 99% confidence interval for the mean mineral yield μY \mu_Y\,μY of these samples.
If six independent random samples are taken and a 99% confidence interval for μ \mu\,μ is constructed for each, find the probability that at least five 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.