In a bioreactor, the dissolved oxygen concentration CCC (mg/L) follows a normal distribution C∼N(μ,σ2)C \sim \mathrm{N}(\mu, \sigma^2)C∼N(μ,σ2). Based on a random sample of measurements, an 80% confidence interval for μ \mu\,μ is determined to be (18.0155,18.7845)(18.0155, 18.7845)(18.0155,18.7845).
Determine a 95% confidence interval for the mean dissolved oxygen concentration μ\muμ.
The total oxygen content in a specific tank volume is given by the linear relationship Q=2.5C+4Q = 2.5C + 4Q=2.5C+4. Using your answer to part (a), calculate a 95% confidence interval for the mean oxygen content μQ\mu_QμQ.
Five independent random samples are collected from different bioreactors with the same mean μ\muμ. A 95% confidence interval for μ \mu\,μ is calculated for each sample. Find the probability that at least four of these five intervals will capture 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.