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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?

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  • $\begingroup$ Welcome to MSE! To correctly format equations use dolar signs and greek letters with back slashes eg $\alpha = \beta$ which renders $\alpha = \beta$. $\endgroup$ – Ali Caglayan Aug 4 '14 at 19:17
  • $\begingroup$ Do you mean expand as in expand out to a series? If so no I did not try that. $\endgroup$ – Sepatau Aug 4 '14 at 19:43
  • $\begingroup$ Still works out to the same value of 1303. I'm beginning to think it's a typo on the provided solution we were given. $\endgroup$ – Sepatau Aug 4 '14 at 19:57
  • $\begingroup$ @chinny84 seems like the answer is correct and it's a difference caused by rounding off. Thanks for help Chinny. $\endgroup$ – Sepatau Aug 4 '14 at 20:25
  • $\begingroup$ Ah the rounding error it sounds like that given the divisor. But great stuff. Write up an answer and accept it to close it off :). $\endgroup$ – Chinny84 Aug 4 '14 at 20:32
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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

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