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.
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.