Suppose the correlation between $x$ and $y$ is $r(x,y) = 0.07$. If the required standard error is equal to 0.33, then the number of required observations will be 1800. I don't know how they find this number of required observations. Because the standard error of a correlation coefficient is $\sqrt{\frac{1-r^2}{n-2}}$. Can anyone let me know how to solve this problem?

  • $\begingroup$ Assuming the equation ${\rm SE} = \sqrt{ (1-r^2)/(n-2) }$ is correct, then you know the relationship. The values of ${\rm SE}$ and $r$ are given in the problem - plug them in and solve for $n$. $\endgroup$ – Macro Mar 28 '13 at 13:10
  • $\begingroup$ @Macro The solution is $n=12$. In order for the solution to be near $1800$, the question has to be modified to read "if the required standard error is equal to $0.33$ times $r(x,y)$, then ..." $\endgroup$ – whuber May 7 '14 at 21:08
  • $\begingroup$ Thank you @whuber. I know n should be 12 but I don't know how they were reported n = 1800. Could you please illustrate your suggestion about question modification? $\endgroup$ – mohammad May 10 '14 at 9:20

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