Could you please help in answering the following question?
The quality control manager at a light globe factory needs to estimate the mean life of large shipment of energy-saving compact light globes. The historical standard deviation of light globe life is 250 hours. A random sample of 64 light globes indicates a sample mean life of 7,940 hours.
a) Construct a 95% confidence interval estimate of the population mean life of light globes in this shipment
b) Do you think that the manufacturer has the right to state that the light globes last on average of 8,000 hours? Explain!
c) Must you assume that the population of light globe life is normally distributed? Explain!
d) Suppose that the standard deviation changes to 180 hours. What are your emended answers in part (a) and (b)?