Question 1126853
Ho: p=0, the correlation is 0
Ha: p NE 0, the correlation is not 0.
If the null hypothesis is rejected, then the conclusion will be that the correlation is not zero.  
There will be a test statistic that will almost certainly not be zero, but the error involved in calculating the test statistic can allow one to calculate the probability that such a value could occur given the null hypothesis. If such a value is highly unlikely (a small p-value) then the null hypothesis might be rejected (depending upon what the critical value was determined beforehand).