A research team wishes to test the null hypothesis: $H_0, r=0$ at $\alpha = 0.025$ against the alternative: $H_1, r>0$ using 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 $\beta = 0.05$ when $r= 0.10$ (that is, $r^2 = 0.01$ ). What is this value?
I used the following equation:
$$n=\frac{Z_{\alpha}+Z_{\beta}}{(0.5\ln(\frac{1+r}{1-r}))}^2+3$$
and got $n\ge1303$, this is different from the answer my professor provided which is $n\ge1320$.
Am I using the correct equation and just plugging in the wrong values or do I have the wrong equation?
The equation is correct and the result is off due to differences in rounding. Use the following values for the variables:
Zalpha = 1.96 Zbeta = 1.645 r = 0.10