1. A city sewer maintenance crew maintained an average of 248 sewer lines per day two years ago. Upon providing more efficient equipment, a sample of 64 sewer-work days shows that a mean of 260 sewer lines were maintained, with a standard deviation of 48 sewer lines. What is the probability that a sample of with this mean could be drawn if the new trucks show no improvement (Note that the population mean is 248)?
2. The failure rate in a community college could jeopardize funding when the rate rises above 20%. The community college district takes a sample of ten schools within the college district and finds the following failure rates: 10.8%, 17.2%, 8.2%, 17.8%, 15.6%, 8.2%, 17.2%, 15.6%, 17.8%, and 10.8%. What is your best estimate of the failure rate in the college district? Is it likely that the failure rate is greater than 20%?
3. The County Department of Children's Services in Bunker County is worried about employee absenteeism. In the previous year, the average employee missed 25.6 days. As a result, an experimental program for which the agency pays employees for each unused sick day or personal day was instituted. A preliminary survey of 40 employees reveals a mean of 17.4 days missed and a standard deviation of 9.6. Present a research hypothesis (alternative hypothesis) and a null hypothesis, and evaluate them.