Answer: There is no evidence of non-zero correlation in the first sample. The least possible value of \(N\) is \(\boxed{9}\).

(i) Use the hypotheses

\[H_0:\rho=0,\qquad H_1:\rho\ne0.\]

Here \(n=15\) and \(r=0.430\). For a two-tailed test at the \(10\%\) significance level, the critical value from the product moment correlation coefficient table is

\[0.441.\]

Since

\[0.430<0.441,\]

we do not reject \(H_0\). There is no evidence, at the \(10\%\) level, of non-zero correlation between the variables.

(ii) Now the test is for positive correlation at the \(5\%\) significance level, so use the one-tailed critical values.

For \(N=8\), the critical value is

\[0.621.\]

Since \(0.615<0.621\), \(N=8\) is not enough.

For \(N=9\), the critical value is

\[0.582.\]

Since \(0.615>0.582\), \(N=9\) is enough to give evidence of positive correlation.

Therefore the least possible value is \(\boxed{9}\).