$X$ and $Y$'s correlation coefficient is $r=0.5$. What is the size of sample when the correlation is significant at $\alpha=0.05$ with two sided test?
Is there a more "formal" way to solve this other than using the "forking" method? In order to solve P-value for the $n$, I will I need $t$, I assume? However, I'm not even sure whether the forking method is allowed in this case since there's a condition $|t|>t_{0.975}(n-2)$ and $P<\alpha$ for the significance.
I'm supposed to find the smallest $n$ where the conditions apply.
edit: I forgot to tell that I am allowed to use Excel as well. However, the functions won't work since I either lack the value of t or n is unknown.
For the two-sided test, when $r=0.5$ you will have significance whenever $|t|>t_{0.975}(n-2)$. So when is this true? You know that $$ t=\frac{r\sqrt{n-2}}{\sqrt{1-r^2}}=\frac{\frac 1 2\sqrt{n-2}}{\sqrt{\frac 3 4}}=\frac{\sqrt{n-2}}{\sqrt 3}. $$ The question then is: for which $n$ is $$ \frac{\sqrt{n-2}}{\sqrt 3}>t_{0.975}(n-2) $$ satisfied? If you're allowed to use Excel, this should not be too much of a problem.