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.
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.