Plastic microparticles are contaminating the world’s shorelines (see Exercise 6.129), and much of this pollution appears to come from fibers from washing polyester clothes. The worst offender appears to be fleece, and a recent study found that the mean number of polyester fibers discharged into wastewater from washing fleece was 290 fibers per liter of wastewater, with a standard deviation of 87.6 and a sample size of 120.
(a) Find and interpret a 99% confidence interval for the mean number of polyester microfibers per liter of wastewater when washing fleece.
(b) What is the margin of error?
(c) If we want a margin of error of only ±5 with 99% confidence, what sample size is needed?

Exercise 6.129

We see that plastic microparticles are contaminating the world’s shorelines and that much of the pollution appears to come from fibers from washing polyester clothes. The same study also took samples from ocean beaches. Five samples were taken from each of 18 different shorelines worldwide, for a total of 90 samples of size 250 mL. The mean number of plastic microparticles found per 250 mL of sediment was 18.3 with a standard deviation of 8.2.