A manufacturer of energy-saving light bulbs claims that their bulbs have a mean lifetime of 1200 hours. A consumer rights group suspects that the actual mean lifetime is less than 1200 hours. They test a sample of 150 bulbs and obtain the following summary statistics:
n=150∑x=178455∑x2=212847914 n = 150 \quad \sum x = 178455 \quad \sum x^2 = 212847914 n=150∑x=178455∑x2=212847914Find the mean and standard deviation of the sample.
Carry out a hypothesis test to test the group's suspicion at the 1% significance level. State your assumptions clearly.
