The Quabbin Reservoir in Massachusetts is 18 miles long and has a capacity of 412 billion gallons. This reservoir serves approximately 2.5 million people, with a daily yield of 300 million gallons of water. The depth of the reservoir is carefully monitored and measured at certain locations and times each day. In a random sample of 18 summer days, the depth (in feet) was measured at location S-1 at noon. The mean depth was 75.4. Assume the population standard deviation is s 5 7.58.
a. Find a 99% confidence interval for the depth of the reservoir at this location.
b. Historical records indicate the mean depth at this location for the previous 10 years is 78.4 feet. Is there any evidence to suggest this population mean has changed?