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...

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
 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?