All problems are to be computed by hand with work shown. Then take a picture or scan your work in and upload it. If you choose to you may type your work up in word.

Question 1:

You want to rent an unfurnished one-bedroom apartment for next semester. The mean monthly rent for a random sample of 10 apartments advertised in the local newspaper is $640. Assume that the standard deviation is $90. Find a 95% confidence interval for the mean monthly rent of an apartment.

Question 2: 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)