Question

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,"† 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.

	Site
Year	1	2	3	4	5	6	7	8	9	10	11	12	13
1982	61.48	64.47	45.50	59.70	58.81	75.86	71.57	38.06	30.51	39.70	29.78	66.89	63.93
1996	13.99	18.26	11.28	10.02	21.00	17.36	28.20	7.30	12.80	9.41	12.63	16.83	22.74

A potential criticism of analyzing these data as if they were two independent samples is that the measurements taken in 1996 were taken at the same site as the measurements taken in 1982. Thus, there is the possibility that there will be a strong positive correlation between the pair of observations at each site.

(a) Plot the pairs of observations in a scatterplot with the 1982 values on the horizontal axis and the 1996 values on the vertical axis.

Does there appear to be a positive correlation between the pairs of measurements?

Yes

No    

(b) Compute the correlation coefficient between the pair of observations.
r =  

Does this value confirm your observations from the scatterplot?

Yes

No    

(c) Answer the following questions using a paired data analysis.(i) 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? (Use α = .05,and let d = 1996 − 1982.)

t	=
tα	=
p-value	=

We fail to reject the null hypothesis and conclude that there has been a significant decrease in the mean PCB content of herring gull eggs.We fail to reject the null hypothesis and conclude that there has not been a significant decrease in the mean PCB content of herring gull eggs.    We reject the null hypothesis and conclude that there has been a significant decrease in the mean PCB content of herring gull eggs.We reject the null hypothesis and conclude that there has not been a significant decrease in the mean PCB content of herring gull eggs.

(ii) Estimate the size of the decrease in mean PCB content from 1982 to 1996, using a 95% confidence interval.
(  ,  )
Are your conclusions different from the conclusions you reached treating the data as two independent samples?

YesNo    

Answer 1