Question: A research team wishes to test the null hypothesis \[{{H}_{0}}:\ \rho =0\] at \[\alpha =0.005\] against the alternative \[{{H}_{1}}:\ \rho >0\] using the Fisher’s transformation of the Pearson product moment correlation coefficient as the test statistic. They have asked their consulting statistician for a sample size n such that \[\beta =0.01\] when \[\rho =0.20\] (that is, \[{{\rho }^{2}}=0.04\] ). What is this number?

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