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

Annual Total Returns (in percent)

Year Energy x Healthcare y 2004 36.65 9.51 2005 44.60 15.41 2006 19.68 10.87 2007 37.00 4.43 2008 -42.87 − 18.45 sx = 35.77 sy= 13.34 sxy = 447.68 Source: w w w . fin a n c e .y a h o o .c o m .

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?