Question

An office building in New York uses thousands of fluorescent light bulb each year. The brand of bulb it currently uses has a mean life of 900 hours. A manufacturer claims that its new brand of bulbs, which cost the same as the brand the office building currently uses, has a mean life of more than 900 hours. The university has decided to purchase the new brand if, when tested, the test evidence supports the manufacturer’s claim at the .05 significance level. Suppose 64 bulbs and the sample has a mean of 920 hours and a standard deviation of 80 hours.
What are the null hypothesis and the alternative hypothesis?
Should the office building purchase the new brand of florescent bulbs? (i.e. test your hypothesis using a z-test)

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The null hypothesis is that there is no difference between the two brands of bulbs. The alternative hypothesis is that the new brand has a life that is longer than 900 hours. In symbols:

H0: L = 900
Ha: L > 900

L is the average life of the new brand of bulbs.

Since we have more than 30 observations, we can use the z-test. The question is, if we assume that the average lifespan of the new bulbs is 900 with a standard deviation of 80, is the observed average of 920 hours consistent with...

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