8 The random variable \(S\) has the distribution \(\mathrm { B } ( 14 , p )\). A significance test is carried out of the null hypothesis \(\mathrm { H } _ { 0 } : p = 0.3\) against the alternative hypothesis \(\mathrm { H } _ { 1 } : p > 0.3\). The critical region for the test is \(S \geqslant 8\).

1. Find the significance level of the test, correct to 3 significant figures.
2. It is given that, on each occasion that the test is carried out, the true value of \(p\) is equally likely to be \(0.3,0.5\) or 0.7 , independently of any other test. Four independent tests are carried out. Find the probability that at least one of the tests results in a Type II error.