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.
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.