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