The article "Quantitative Estimation of Clay Mineralogy in Fine-Grained Soils" (J. of Geotechnical and Geoenvironmental Engr., 2011: 997-1008) reported on various chemical properties of natural and artificial soils. Here are observations on x = cation exchange capacity (CEC, in meq/100 g) and y = specific surface area (SSA, in m2/g) of 20 natural soils.

Minitab gave the following output in response to a request for r: correlation of x and y = 0.853
Normal probability plots of x and y are quite straight.
a. Carry out a test of hypotheses to see if there is a positive linear association in the population from which the sample data was selected.
b. With n = 20, how small would the value of r have to be in order for the null hypothesis in the test of (a) to not be rejected at significance level .01?
c. Calculate a confidence interval for ( using a 95% confidence level.

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66 121 134 101 77 89 63 57 117 118 y 175 324 460 288 205 210 295 161 314 265 x 76 125 75 71 133 104 76 96 58 109 y 236 355 240 133 431 306 132 269 158 303