The lifespans of high-performance LED modules tested under extreme thermal stress are recorded. A random sample of 15 modules yields a mean lifespan of 1250 hours1250\text{ hours}1250 hours. The lifespans are known to follow a normal distribution with a population standard deviation of 45 hours45\text{ hours}45 hours.
Estimate the bounds within which 90%90\%90% of the lifespans of individual modules are expected to fall.
Construct a 95%95\%95% confidence interval for the population mean lifespan μ\muμ of these modules.
An engineer asserts that the true mean lifespan of these modules under these conditions is 1280 hours1280\text{ hours}1280 hours.
Evaluate the engineer's assertion based on your result in part (b). Provide a mathematical justification.
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.