# An office building in New York uses thousands of fluorescent light ...

## 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 manufacturerâ€™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)

## Solution Preview

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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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