2. PCB\'s are a known environmental contaminant and their use was restricted in

Question

2. PCB's are a known environmental contaminant and their use was restricted in the 1970's. The mean PCB content in gull eggs was taken at 13 sites around the Great Lakes in 1982 and again in 1996 at these same sites. A subset of the data are below. A two-sided paired T-test is run on the data and a p-value of 1.01 × 10-7 is obtained. Site 1 Site 2 Site 3 Site 4 … 1982: 61.48 64.47 45.50 59.70... 1996: 13.99 18.26 11.28 10.02 (a) By running a paired T-test, what source of variability is accounted for? (b) If an independent two-sample T-test were run instead, would the p-value be larger or smaller?

Explanation / Answer

a ) A paired t test is used to compared 2 sets of data and determine if the mean difference between these 2 sets is zero

Hence the paired t test checks if variation in the mean differences is zero or non zero of the 2 set of data in consideration

b) We are given that the p value of th paired t test is 1.01 * 10^-17 which is very significant

as 1.01 * 10^-17 < 0.05 (considering 5% level of significance)

So the p value suggests that paired sampling is better

Hence a independent 2 sample t test would give us a larger p value

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