A company producing light bulbs wishes to claim that their light bulbs last more

900 hours. To test this claim, the company took a random sample of 1000 ( = 1000) from those it has

produced and found that the average lifetime for this sample is 884 burning hours (< = 884). The

company knows that the standard deviation of the lifetime of light bulbs is 91 hours ( = 91). Can the

company claim that the average lifetime of its light bulbs is more than 900 hours?

To answer this question, you need to find the posterior distribution and then use it to test

!: 900 vs ": > 900

Note: because there is no previous information is available, you should use Jeffrey's prior as a

reference prior.