1.1. In the context of hypothesis testing, explain the term:

(i) critical region

(ii) critical value

1.2. The table below shows the probabilities for different values that $X\textasciitilde{}B(40,0.8)$can take:

A test of the null hypothesis  ${H}_{0}:p=0.8$ against the alternative hypothesis ${H}_{1}∶p>0.8$ is carried out for the random variable $X\textasciitilde{}B(40,p).$

 Using a 5% level of significance, find the values of $X$ which would lead to the rejection of the null hypothesis.

1.3. A second test is carried out with the same null hypothesis against the alternative hypothesis ${H}_{1}∶p\neq0.8.$

Given that $x=38$ is a critical value, find the minimum level of significance for the test.