A group of investors wants to develop a chain of fast-food

Question 1
 

A group of investors wants to develop a chain of fast-food restaurants. In determining potential costs
for each facility, they must consider, among other expenses, the average monthly electric bill. They
decide to sample some fast-food restaurants currently operating to estimate the monthly cost of
electricity. They want to be 90% confident of their results and want the error of the interval estimate to
be no more than $100. They estimate that such bills range from $600 to $2,500. How large a sample
should they take?

Question 2
 

Suppose a study reports that the average price for a gallon of self-serve regular unleaded gasoline is
$3.16. You believe that the figure is higher in your area of the country. You decide to test this claim
for your part of the United States by randomly calling gasoline stations. Your random survey of 25
stations produces the following prices (all in $). Assume gasoline prices for a region are normally
distributed. Do the data you obtained provide enough evidence to reject the claim? Use a 1% level of
significance.
3.27 3.29 3.16 3.20 3.37
3.20 3.23 3.19 3.20 3.24
3.16 3.07 3.27 3.09 3.35
3.15 3.23 3.14 3.05 3.35
3.21 3.14 3.14 3.07 3.10