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.
Practise Edexcel A Level Maths The Normal Distribution with exam-style questions for A Level Maths. 100 questions covering The Normal Distribution, Finding Probabilities for Normal Distributions, The Inverse Normal Distribution Function, The Standard Normal Distribution, Finding the mean and standard deviation, Approximating a Binomial Distribution, and Hypothesis Testing with the Normal Distribution, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.