You invest your lifes savings in 5 di?erent hedge fund companies, each of which

Question

You invest your lifes savings in 5 di?erent hedge fund companies, each of which invests your money in 10 di?erent in-house funds. You realize that this type of investing is risky, but you want the maximum long-term growth rate. After one year, the results are as listed in the table. Are the hedge fund companies equally good, or are there statistically signi?cant di?erences between them?

Note: the standard deviation for each company was computed as

where n = 10 and x is the average for that company.

Company Average return(%) Std. dev. (%) 4.0 10.6 5.9 7.1 7.7 6.8 7.8 8.2 6.5 2.4

Explanation / Answer

Here we want to compare the more than 2 popualtion means so ANOVA will be used. Hypotheses are:

H0: the hedge fund companies are equally good.

Ha: the hedge fund companies are not equally good.

Following is the output of ANOVA:

Since p-value of the test is 0.149 which is greater than 0.05 so we fail to reject the null hypothesis. That is we can conclude that the hedge fund companies are equally good.

Source of Variation Sum of Squares d.f. Variance F p Between Groups: 393.4 4 98.35 1.7826 0.149 Within Groups: 2482.74 45 55.172 Total: 2876.14 49

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