The quality control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7,500 hours. The population standard deviation is 1,000 hours. A random sample of 64 CFLs indicates a sample mean life of 7,250 hours.

a. At the 0.05 level of significance, is there evidence that the mean life is different from 7,500 hours?

b. Compute the p value and interpret its meaning. 

c. Construct a 95% confidence interval estimate of the population mean life of the CFLs.

d. Compare the results of (a) and (c). What conclusions do you reach?