Selected mutual funds that practice socially aware investing, with year-to-date rates of return, are shown in Table 10.7.3. On average, these funds lost value in the first half of 2010, in the sense that their average rate of return was negative. However, the Standard & Poor€™s 500 stock market index lost 9.03% of its value during the same period, so this was a difficult time for the market in general.
a. On average, as a group, did socially aware mutual funds lose significantly more than the market index? Please use the market index as the reference value.
b. Find the p-value for this test (as either p > 0.05, p c. Identify the underlying hypotheses and assumptions involved in part a.
d. Under these assumptions, the hypothesis test makes a clear and correct statement. However, are the assumptions realistic? Be sure to address independence (note that some of these funds are part of the same group).
e. Why is a two-sided test appropriate in this case?
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TABLE 10.7.3 Performance of Socially Aware Investment Funds Rate of Return un Calvert Global Alternative Energy Fund A 26.9 Calvert Global Water Fund Calvert New Vision Small Cap A Calvert Social Investment Balanced A Calvert World Values International A Domini Social Equity A Gabelli SRI Green Fund Inc A Green Century Balanced Legg Mason Prt Social Awareness Fund A Neuberger Berman Socially Resp Inv Pax World Global Green Fund-Individual -10.35% Investor Sentinel Sustainable Core Opportunities Fund TIAA-CREF Social Choice Eq Retail Walden Social Balanced Fund Winslow Green Growth Fund 9.28% -5.42% -2.16% -11 .07% 4.38% -16.32% -4.00% -4 27% -0.53% -7.38% -5.98% -275% -15.59%