8 The random variable \(R\) has the distribution \(\mathrm { B } ( 10 , p )\). The null hypothesis \(\mathrm { H } _ { 0 } : p = 0.7\) is to be tested against the alternative hypothesis \(\mathrm { H } _ { 1 } : p < 0.7\), at a significance level of \(5 \%\).
- Find the critical region for the test and the probability of making a Type I error.
- Given that \(p = 0.4\), find the probability that the test results in a Type II error.
- Given that \(p\) is equally likely to take the values 0.4 and 0.7 , find the probability that the test results in a Type II error.