Question: The following table shows the annual returns for two of Vanguard's mutual funds: the Vanguard Energy Fund and the Vanguard Healthcare Fund. a. Calculate and

The following table shows the annual returns for two of Vanguard's mutual funds: the Vanguard Energy Fund and the Vanguard Healthcare Fund.

a. Calculate and interpret the sample correlation coefficient rxy.
b. Specify the competing hypotheses in order to determine whether the population correlation coefficient is significantly different from zero.
c. At the 5% significance level, what is the conclusion to the test? Are the returns on the mutual funds significantly correlated?

Annual Total Returns (in percent) Year 2004 2005 2006 2007 2008 Energy X 36.65 44.60 19.68 3700 -42.87 19.01 S 35.7)7 ealthcare y 9.51 15.41 10.87 4.43 -18.45 y 4.35 sy 13.34 Sry-44768

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