Solutions Statistics

Here is the data on the annual returns (percent) for the Vanguard International Growth Fund and its

Question: Here is the data on the annual returns (percent) for the Vanguard International Growth Fund and its benchmark index, the Morgan Stanley EAFE index. Doe the fund significantly outperform its benchmark?

(a) Explain clearly why the matched pairs t test is the proper choice to answer this question.

(b) Make a stemplot of the differences (fund-EAFE) for the 20 years. There is no reason to doubt the approximate Normality of the differences. (More detailed study shows that the differences follow a Normal distribution quite closely.)

Year	Fund	EAFE	Year	Fund	EAFE
1982	5.27	-1.86	1992	-5.79	-12.17
1983	43.08	23.69	1993	44.74	32.56
1984	-1.02	7.38	1994	0.76	7.78
1985	56.94	56.16	1995	14.89	11.21
1986	56.71	69.44	1996	14.65	6.05
1987	12.48	24.63	1997	4.12	1.78
1988	11.61	28.27	1998	16.93	20
1989	24.76	10.54	1999	26.34	26.96
1990	-12.05	-23.45	2000	-8.6	-14.17
1991	4.74	12.13	2001	-18.92	-21.44