The following table shows the sample correlations between the monthly returns for four different mutual funds and the S&P 500. The correlations are based on 36 monthly observations.
The funds are as follows:
Fund 1 ...............................Large-cap fund
Fund 2................................Mid-cap fund
Fund 3................................Large-cap value fund
Fund 4................................Emerging markets fund
S&P 500.............................US domestic stock index

Test the null hypothesis that each of these correlations, individually, is equal to zero against the alternative hypothesis that it is not equal to zero. Use a 5 percent significance level.

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Fund 2 Fund 3 Fund 4 S&P 500 Fund 1 Fund 1 Fund 2 0.9231 Fund 3 0.4156 0.4771 1 Fund 4 0.3102 0.7238 1 0.7111 S&P 500 0.5791 0.8223 0.8277 0.7515