The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The manufacturer's specifications are that the standard deviation is 100 hours. A random sample of 64 light bulbs indicated a sample mean life of 350 hours.
a. Construct a 95% confidence interval estimate for the population mean life of light bulbs in this shipment.
b. Do you think that the manufacturer has the right to state that the light bulbs have a mean life of 400 hours? Explain.
c. Must you assume that the population light bulb life is normally distributed? Explain.
d. Suppose that the standard deviation changes to 80 hours. What are your answers in (a) and (b)?