Question: A manufacturer of replacement bulbs for LCD projectors claims a 1000 hour average life time for the bulbs. This is important, since the bulbs sell for around $300 each. Concerned that the claim may not be valid because of a recently discovered problem in the manufacturing process, the company decides to test it. Twelve bulbs are randomly selected from a production run, each is burned until it fails, and its lifetime recorded. Here are the 12 lifetimes, in hours.

1005 987 1035 1000 1005 1032 1001 999 1019 985 1011 1009

What do these 12 lifetimes suggest about the manufacturer’s claim? Be specific about assumptions, hypotheses being tested, test statistic used, and the critical region for your test. Interpret the results of your test in regard to the claim of the bulb manufacturer. (You may do this test by hand or get SPSS to do it for you. If you use SPSS, please provide the output it produces along with your interpretation of the results.) Note that you have not been asked for nor should you consider a confidence interval in this problem.

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