Question 8.74

74. Herbicide Concentration. Human exposure to herbicides is a potential hazard in America's grain-producing areas. One study found that, in a random sample of 112 homes in Iowa, the median concentration of the herbicide dicamba was 179.5 ng/g (nanograms per gram).7 Suppose that the sample mean was 180 ng/g, and assume that the population standard deviation is 20 ng/g.

  1. Compute and interpret the margin of error for a confidence interval with 95% confidence.
  2. Construct and interpret a 95% confidence interval for the population mean concentration of the herbicide dicamba in Iowa homes.
  3. How large a sample size is needed to estimate to within 3.7 ng/g with 95% confidence? Comment.
  4. How large a sample size is needed to estimate to within 3.7 ng/g with 99% confidence?