1. A local environmental agency has selected a simple random sample of 16 homes to be tested for tap-water lead. Concentrations of lead were found to have a mean of 12 parts per billion and a standard deviation of 4 parts per billion. Considering that the homes were selected from a community in which there are 100 homes, construct and interpret the 95% confidence interval for the population mean. Based on your results, comment on the possibility that the average lead concentration in this community's homes might exceed the Environmental Protection Agency's recommended limit of 15 parts per billion of lead.
2. A simple random sample is to be drawn from a population of 800. In order to have 95% confidence that the sampling error in estimating 7T is no more than 0.03, what sample size will be necessary?