Chapter 13.3, Problem 1Q

Case Study 7.5.2 compared the volatility of Global Rock Funds’ return on investments to that of the bench-mark Lipper fund. But can it be said that the returns them-selves beat the benchmark? The table below gives the annual returns of the GlobalRock Fund for the years 1989 to 2007 and the corresponding Lipper averages. Test the hypothesis that ${\text{μ}}_D>0$ for these data at the 0.05 level of significance.

Investment Return %Investment Return %
Year	Global Rock, x	Lipper Avg., y	Year	Global Rock, x	Lipper Avg., y
1989	15.32	14.76	1999	27.43	34.44
1990	1.62	-1.91	2000	8.57	1.13
1991	28.43	20.67	2001	1.88	-3.24
1992	11.91	6.18	2002	-7.96	-8.11
1993	20.71	22.97	2003	35.98	32.57
1994	-2.15	-2.44	2004	14.27	15.37
1995	23.29	20.26	2005	10.33	11.25
1996	15.96	14.79	2006	15.94	12.70
1997	11.12	14.27	2007	16.71	9.65
1998	0.37	6.25

Note that ${\displaystyle \underset{i=1}{\overset{19}{\sum }}{d}_i=28.17}$ ${\displaystyle \underset{i=1}{\overset{19}{\sum }}{d}_i^2=370.8197}$