Refer to Exercise 6.11. There appears to be a large variation in the mean PCB content ac...

Refer to Exercise 6.11. There appears to be a large variation in the mean PCB content across the 13 sites. How could we reduce the effect of variation in PCB content due to site differences on the evaluation of the difference in the mean PCB content between the two years?

REFERENCE:

6.11: PCBs have been in use since 1929, mainly in the electrical industry, but it was not until the 1960s that they were found to be a major environmental contaminant. In the paper “The ratio of DDE to PCB concentrations in Great Lakes herring gull eggs and its use in interpreting contaminants data” [appearing in the Journal of Great Lakes Research 24 (1): 12–31, 1998], researchers report on the following study. Thirteen study sites from the five Great Lakes were selected. At each site, 9 to 13 herring gull eggs were collected randomly each year for several years. Following collection, the PCB content was determined. The mean PCB content at each site is reported in the following table for the years 1982 and 1996.

a. Legislation was passed in the 1970s restricting the production and use of PCBs. Thus, the active input of PCBs from current local sources has been severely curtailed. Do the data provide evidence that there has been a significant decrease in the mean PCB content of herring gull eggs?

b. Estimate the size of the decrease in mean PCB content from 1982 to 1996, using a 95% confidence interval.

c. Evaluate the conditions necessary to validly test hypotheses and construct confidence intervals using the collected data.

d. Does the independence condition appear to be violated?