(a) Which test would be more appropriate in this case: a t-test for the difference between two population means, or a paired t-test? Why? (b) Do the data provide sufficient evidence to support the claim that the mean PCB level has decreased in the region? Be sure to check all assumptions, write the null and alternative hypotheses, calculate the appropriate test statistic, calculate the p-value, and state your conclusion. (c) Construct a 95% confidence interval for the mean decrease in PCB level.
widely used as dielectrics and coolants in electrical systems in the past. They were found to be a major environmental contaminant in the 1960s. In a study, the mean PCB content at each of thirteen sites was reported for the years 1982 and 1996 (from “The ratio of DDE to PCB concentrations in Great Lakes herring gull eggs and its use in interpreting contaminants data”, Journal of Great Lakes Research 24 (1): 12-31, 1998). The data are below.
Site:
1
2
3
4
5
6
7
8
9
10
11
12
13
1982
61.48
64.47
45.50
59.70
58.81
75.96
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) Which test would be more appropriate in this case: a t-test for the difference between two population means, or a paired t-test? Why?
(b) Do the data provide sufficient evidence to support the claim that the mean PCB level has decreased in the region? Be sure to check all assumptions, write the null and alternative hypotheses, calculate the appropriate test statistic, calculate the p-value, and state your conclusion.
(c) Construct a 95% confidence interval for the mean decrease in PCB level.
Trending now
This is a popular solution!
Step by step
Solved in 4 steps