Polychlorinated biphenyls (PCBs) are a group of synthetic oil-like chemicals whose toxicity was first recognized in the 1970s. Until then, they were widely used as insulation in electrical equipment, particularly transformers. PCB concentrations in bird eggs helps researchers quantify bioaccumulation of PCBs in ecosystems. Thirteen sites in the Great Lakes were selected for a study to quantify PCB concentrations in 1982 and 1996 (Hughes et al. 1998). At each site, 9-13 American herring gull (Larus smithsonianus) eggs were randomly collected and tested for PCB content. Test to see if 1996 levels were lower than 1982 levels using a two-sample t -test that assumes unequal variances. Use α= 0.01. Assume for 1982 the sample mean is 54.33 and variance is 245.08. Assume for 1996 the sample mean is 15.53 and variance is 35.56.
a) Correctly state the hypotheses in terms of population parameters.
b) Calculate the degrees of freedom, ν, by hand.
c) Calculate the test statistic by hand.
d) Calculate the p-value by hand.
