data4 = Import["http://pmaweb.caltech.edu/~phy003/labs/Data1.txt", "TSV"]

dta4a = Rest[data4]

data4at = Transpose[dta4a]

PearsonCorrelationTest[data4at[[1]], data4at[[2]], "TestDataTable"]

PearsonCorrelationTest[data4at[[1]], data4at[[2]], "TestConclusion", SignificanceLevel -> 0.01]

IndependenceTest[data4at[[1]], data4at[[2]], {"TestDataTable", All}]

CorrelationTest[dta4a,0.05,  "TestDataTable"]

IndependenceTest[{1,2,3,4,5}, {4,6,3,0,2}, {"TestDataTable", All}]

IndependenceTest[{1,2,3,4,5}, {8,8,5,6,3}, {"TestDataTable", All}]

Problem 9.16a

PearsonCorrelationTest[{1,2,3,4,5}, {8,8,5,6,3}, "TestConclusion"]

PearsonCorrelationTest[{1,2,3,4,5}, {8,8,5,6,3}, "TestConclusion", SignificanceLevel -> 0.01]

Problem 9.16b

PearsonCorrelationTest[{1,2,3,4,5}, {4,6,3,0,2}, "TestConclusion"]

PearsonCorrelationTest[{1,2,3,4,5}, {4,6,3,0,2}, "TestConclusion", SignificanceLevel -> 0.01]