Question: National Recycling operates a garbage hauling facility in a southern Maine city. Each year the company must apply for a new contract with the state. The contract is in part based on the pounds of recycled materials collected. Part of the analysis that goes into contract development is an estimate of the mean pounds of recycled materials submitted by each customer in the city on a quarterly basis. If 6 months after the contract has been signed, the actual mean pounds deviate from the estimate, an adjustment will be made (up or down) in the amount National Recycling receives. As such, suppose that a random sample of National Recycling’s customers are selected (n=100) and the sample mean is 40.78 lbs. Assume that from past years, the population standard deviation is known to be 12.6 lbs.

a. Suppose the city has asked for a 95% confidence interval estimate for the true population mean. Calculate that confidence interval.

b. Suppose that 6 months later, the actual mean pounds of garbage collected is 37.98 lbs. Based on your answer, will the city adjust their contract up or down? How can you tell?