I disagree with the answer they give.
P(X=0) = 0.01889(4.s.f) > 0.01=1%. Going back to the definition of "critical region", and comparing to the example on page 101/102 (which I will not post here for brevity):
Now it would be "surprising/unlikely" to get 0 successes given X~B(20,0.18). However, 1.889% is not "less than 1% (un)likely", and so if we carried out these 20 trials and got 0 successes, surely we would not reject the null hypothesis at the 1% significance level.
So ultimately the answer should be: "Assume Ho is true. Then X~B(20,0.18). We would not reject the null hypothesis at the 1% significance level, even if our test statistic turned out to be X=0, because p(X=0) = 0.82^20 = 0.01889(4.s.f)> 0.01=1%. Therefore there is no critical value and therefore no critical region at such a low significance level as 1%, and we would have to accept Ho for all possible test statistics 0<=X<=20".
For those without access to the book and who aren't sure what is meant by "test statistic", quoting the book, "The result of the experiment or the statistic that is calculated from the sample is called the test statistic".
Am I right or is there a flaw in my reasoning here?
Thanks in advance.