The Following Data for Five Years of the Annual Returns

Multiple Choice

The following data for five years of the annual returns for two of Vanguard's mutual funds, the Vanguard Energy Fund (x) and the Vanguard Healthcare Fund (y) , were given as s_x = 35.77, s_y = 13.34, s_xy = 447.68. The competing hypotheses are H₀: ρ_xy = 0, H_A: ρ_xy ≠ 0. At the 5% significance level which of the following is the correct conclusion to the test?

A) Reject the null hypothesis; we can conclude that the returns of these two mutual funds are correlated.
B) Reject the null hypothesis; we cannot conclude that the returns of these two mutual funds are not correlated.
C) Do not reject the null hypothesis; we can conclude that the returns of these two mutual funds are correlated.
D) Do not reject the null hypothesis; we cannot conclude that the returns of these two mutual funds are correlated