The lengths of steel rods, XXX cm, have a normal distribution with unknown mean μ\muμ cm and known standard deviation σ\sigmaσ cm. A random sample of 64 rods yielded a 95% confidence interval for μ\muμ of (12.18,12.62)(12.18, 12.62)(12.18,12.62).
Without carrying out any further calculations, use this confidence interval to test whether or not μ=12.7\mu = 12.7μ=12.7. State your hypotheses clearly and write down the significance level you have used.
A second random sample, of 80 rods, had a mean length of 12.4512.4512.45 cm.
Calculate a 99% confidence interval for μ\muμ based on this second sample.
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.