Mutual funds often compare their performance with a benchmark provided by an "index" that describes the performance of the class of assets in which the fund invests. For example, the Vanguard International Growth Fund benchmarks its performance against the EAFE (Europe, Australasia, Far East) index. The table below gives the annual returns (percent) for the fund and the index. Does the fund's performance differ significantly from that of its benchmark?
(a) Explain clearly why the matched pairs t test is the proper choice to answer this question.
(b) Do a complete analysis for the question that is posed here.
A Mutual Fund Versus its Benchmark Index
Year Fund Return Index Return Year Fund Return Index Return
1982 5027 -1.86 1994 0.76 7.78
1983 43.08 23.69 1995 14.89 11.21
1984 -1.02 7.38 1996 14.65 6.05
1985 56.94 56.16 1997 4.12 1.78
1986 56.71 69.44 1998 16.93 20
1987 12.48 24.63 1999 26.34 26.96
1988 11.61 28.27 2000 -8.6 -14.17
1989 24.76 10.54 2001 -18.92 -21.44
1990 -12.05 -23.45 2002 -17.79 -15.94
1991 4.74 12.13 2003 34.45 38.59
1992 -5.79 -12.17 2004 18.95 20.25
1993 44.74 32.56 2005 15 13.54