The quality control manager at a light bulb factory needs to estimate the average life of a large shipment of light bulbs. A random sample of 64 light bulbs indicated a sample average life of 300 hours with a sample standard deviation of 100 hours.
(a) Set up a 95% confidence interval estimate of the true average life of light bulbs in this shipment.
(b) Do you think the manufacturer has the right to state that the light bulbs last an average of 400 hours? Justify your answer.
(c) Explain why an observed value of 250 hours is not unusual for an individual light bulb, even though it is outside the confidence interval you calculated.