A sample of n = 500(x, y) pairs was collected and a test of H0: ρ = 0 versus Ha: ρ ≠ 0 was carried out. The resulting P-value was computed to be .00032.
a. What conclusion would be appropriate at level of significance .001?
b. Does this small P-value indicate that there is a very strong linear relationship between x and y (a value of ρ that differs considerably from 0)? Explain.
c. Now suppose a sample of n = 10, 000(x, y) pairs resulted in r = .022 . Test H0: ρ = 0 versus Ha: ρ ≠ 0 at level .05. Is the result statistically significant? Comment on the practical significance of your analysis.
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