Consider the data in the following table.

a. Find the sample correlation coefficient r. Interpret your result.
b. Show that the test statistic T = β1/(Sy|x / Sxˆšn - 1) for testing H0: β1 = 0 (based on a straight-line regression relationship between Y and X) is exactly equivalent to the test statistic Tʹ = r ˆšn €“ 2 / ˆšl €“ r2 for testing H0: p = 0. Use β1 = rSy/Sx and

c. Using T', test H0: p = 0 versus HA: p ‰  0.
d. Despite the conclusion you obtained in part (c), why should you be reluctant to conclude that the two variables are linearly related?

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