The quality control manager at a light globe factory needs to estimate the mean life of a large shipment of energy-saving compact fluorescent (CFL) light globes. As- sume that the standard deviation is 250 hours. A random sample of 64 light globes indicates a sample mean of 7,930 hours.

(a) Do you think that the manufacturer is incorrect to state that the light globes last an average of at least 8,000 hours? You should justify your answer with a hypothesis test at the 5% significance level.

(b) Construct a 95% confidence interval estimate of the population mean life of light globes in this shipment.

(c) Do you need to assume that the population of light globe life is normally distributed in your answers to Parts (a) and (b). You should give a brief explanation of your answer.