# Question

The package of Sylvania CFL 65-watt replacement bulbs that use only 16 watts claims that these bulbs have an average life of 8000 hours. Assume that the standard deviation of lives of these light bulbs is 400 hours. A skeptical consumer does not think that these light bulbs last as long as the manufacturer claims, and she decides to test 52 randomly selected light bulbs. She has set up the decision rule that if the average life of these 52 light bulbs is less than or equal to 7890 hours, then she will reject company’s claim and conclude that the company has printed too high an average life on the packages, and she will write them a letter to that effect. Approximately what significance level is she using? If she decides instead on the decision rule that if the average life of these 52 light bulbs is less than or equal to 7857 hours she will reject the null hypothesis that company’s claim is true, then approximately what significance level is she using? Interpret the values you get.

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