Problem 5: Paired T-Test The following table shows the outcome of eight years of a ten year bet that Warren Buffett placed with Protege Partners, a New York hedge fund. Buffett claimed that a simple index fund would beat a portfolio strategy (fund-of-funds) picked by Protege over a ten year time frame. At Buffett's shareholder meeting, he provided an update of the current state of the bet. The bundle of hedge funds picked by Protege had returned 21.9% in the eight years through 2015 and the S&P500 index fund had soared 65.7%. SP Index Hedge Funds 2008 -37.0% 23.9% 2009 26.6% 15.9% 2010 15.1% 8.5% 2011 2.1% -1.9% 2012 16.0% 6.5% 2013 32.3% 11.8% 2014 13.6% 5.6% 2015 1.4% 1.7% cumulative 65.7% 21.9% (a) Use a paired t-test to assess the statistical significance between the two return strategies (b) How likely is Buffett to win his bet in two years