A brand of LED lightbulbs claims to have a mean lifespan of 1200 hours.
An electrical engineer believes that the actual mean lifespan is less than 1200 hours.
The engineer tests a large batch of bulbs and produces the following summary data:
n=300∑x=357900∑x2=427454700 n = 300 \quad \sum x = 357900 \quad \sum x^2 = 427454700 n=300∑x=357900∑x2=427454700Find the mean and standard deviation of the sample.
Carry out a hypothesis test to test the engineer's belief at the 1% significance level. State your assumptions clearly.
390 exam-style questions on OCR A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.