3 A package of light bulbs promises an average life of more

3. 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 a = 30 hours. The manufacturer responded that its claim was based on testing hundreds of bulbs. (a) [Free Response] If the consumer group and the manufacturer both make 95% confidence intervals for the population\'s average lifetime, whose will probably be shorter? Can you tell for certain? (b) [True or False] Given the usual sampling assumptions, there is a 95% probability that 740 lies in the 95% confidence interval of the manufacturer. (c) [Free Response] Is the manufacturer\'s confidence interval more likely to contain the population mean because it is based on a larger sample?

Solution

a) consumer\'s

b)False.

c)yes.