The following table shows a portion of the monthly returns data (in percent) for 2010–2016 for two of Vanguard’s mutual funds: the Vanguard Energy Fund and the Vanguard Healthcare Fund.

a. Calculate and interpret the sample correlation coefficient r_xy.

b. Specify the competing hypotheses in order to determine whether the population correlation coefficient is different from zero.

c. At the 5% significance level, what is the conclusion to the test? Are the returns on the mutual funds correlated?

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Date Energy Healthcare -4.86 -0.13 Jan-10 Feb-10 1.50 0.58 Dec-16 -0.30 -5.26