The lifespan of high-performance LED modules is normally distributed with an unknown mean, μ\muμ hours, and a known standard deviation, σ\sigmaσ hours. A random sample of 150 modules yields a 98% confidence interval for μ\muμ of
(2491.56,2508.44) (2491.56, 2508.44) (2491.56,2508.44)Using the confidence interval provided, test whether or not μ=2500\mu = 2500μ=2500. State your hypotheses clearly and the significance level used.
A second random sample of 200 modules had a mean lifespan of 2505 hours.
Calculate a 99% confidence interval for μ\muμ based on this second sample. You must show all steps in your working.
Using eight different random samples of 200 modules, eight 99% confidence intervals for μ\muμ are to be found.
Calculate the probability that at least 7 of these intervals will contain 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.