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...

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?

Rising costs caused many Americans to do without health insurance. A random sample of adults of various ethnicities was obtained and asked whether they had health insurance. The resulting data are given in the table below.

a. Find a 95% confidence interval for the proportion of adults without health insurance for each group

b. A government publication claims that the proportion of people without health insurance for the general population is 0.146. Using the confidence intervals in part (a), is there evidence that any group has a different population proportion without health insurance?