A package of light bulbs promises an average life of more than 750 hours per bulb. A consumer group did not believe the claim and tested a sample of 40 bulbs. The average lifetime of these 40 bulbs was 740 hours with s = 30 hours. The manufacturer responded that its claim was based on testing hundreds of bulbs.
(a) If the consumer group and manufacturer both make 95% confidence intervals for the population’s average lifetime, whose will probably be shorter? Can you tell for certain?
(b) Given the usual sampling assumptions, is there a 95% probability that 740 lies in the 95% confidence interval of the manufacturer?
(c) Is the manufacturer’s confidence interval more likely to contain the population mean because it is based on a larger sample?