A Sample of N = 500 (X, Y) Pairs Was $H _ { o } : \rho = 0 \text { versus } H _ { \pm } : \rho \neq 0$

Essay

A sample of n = 500 (x, y) pairs was collected and a test of $H _ { o } : \rho = 0 \text { versus } H _ { \pm } : \rho \neq 0$ 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 $\rho$
that differs considerably from 0)?
Explain.