The accompanying table shows annual return data from 20012009 for Vanguards Balanced Index and European Stock Index

The accompanying table shows annual return data from 2001–2009 for Vanguard’s Balanced Index and European Stock Index mutual funds. The data set, labeled Balanced_European, can also be found on the text website.

Assume that returns are normally distributed.

a. Set up the hypotheses to test whether the mean returns of the two funds differ.
b. What are the value of the test statistic and its associated p -value given unequal population standard deviations?
c. At the 5% significance level, what is theconclusion?

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Balanced Index Year 2001 2002 2003 2004 2005 2006 2007 2008 2009 3.02% 9.52 19.87 9.33 4.65 11.02 6.16 22.21 20.05 European Index 20.30% 17.95 38.70 20.86 9.26 33.42 13.82 44.73 31.91