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20.48 Mutual funds performance. Mutual funds often compare their performance with a benchmark pro- vided by an "index" that describes the performance of the class of assets in which the fund invests. For ex- ample, the Vanguard International Growth Fund benchmarks its performance against the Spliced Inter- national Index. Table 20.3 gives annual returns (per- cent) for the fund and the index. Does the fund's performance differ significantly from that of its benchmark? MFUND (a) Explain clearly why the matched pairs t test is the proper choice to answer this question. (b) Do a complete analysis that answers the question posed. TABLE 20.3 A mutual fund versus its benchmark index Fund Index Fund Index Fund Return Return Return Return Return Year (%) (%) Year (%) (%) Year (%) 1984 - 1.02 7.38 1992 -5.79 -12.17 2000 -8.60 1985 56.94 56.16 1993 44.74 32.56 2001 - 18.92 1986 56.71 69.44 1994 0.76 7.78 2002 - 17.79 1987 12.48 24.63 1995 14.89 11.21 2003 34.45 1988 11.61 2 8.27 1996 14.65 6.05 2004 18.95 1989 24.76 10.54 1997 4.12 1.78 2005 15.00 1990 -12.05 - 23.45 1998 16.93 20.00 2006 25.92 1991 4.74 12.13 1999 26.34 26.96 2007 15.98 Index Return (%) -- 14.17 -21.44 -15.94 38.59 20.25 13.54 26.34 1 1.17 Year 2008 2009 2010 2011 2012 2013 2014 2015 Fund Return (%) -44.94 41.63 15.66 - 13.68 20.01 22.95 -5.63 -0.67 Index Return (%) -43.38 31.78 8.13 -13.71 16.83 15.29 -3.87 -5.66