In this exercise, a randomization distribution is given for a hypothesis test, and shows what values of the sample statistic are likely to occur if the null hypothesis is true. Several possible values are given for a sample statistic. In each case, indicate whether seeing a sample statistic as extreme as the value given is (i) reasonably likely to occur when the null hypothesis is true, (ii) unusual but might occur occasionally when the null hypothesis is true, or (iii) extremely unlikely to ever occur when the null hypothesis is true.
The figure below shows a randomization distribution for a hypothesis test with
$H_0: p = 0.30$.
(a) $\hat{p} = 0.48$
(i) Reasonably likely to occur when the null hypothesis is true.
(ii) Unusual but might occur occasionally when the null hypothesis is true.
(iii) extremely unlikely to ever occur when the null hypothesis is true.
