Question: The operations manager at a light bulb company wants to determine whether there is any difference in the mean life expectancy of LED bulbs manufactured on two different types of machines. The population standard deviation of machine (1) is 29,300 hours and of machine (2) is 34,500 hours. A random sample of 25 light bulbs from machine (1) indicates a sample mean of 100,000 hours, and a similar sample of 25 from machine (2) indicates a sample mean of 95,500 hours.

Required:

a) Using the 0.05 level of significance, is there any evidence of a difference in the mean life of bulbs?

b) Calculate the P- value in a) and interpret its meaning.