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.
