6. (a) Define the critical region of a test statistic. A discrete random variable \(X\) has a Binomial distribution \(\mathrm { B } ( 30 , p )\). A single observation is used to test \(\mathrm { H } _ { 0 } : p = 0.3\) against \(\mathrm { H } _ { 1 } : p \neq 0.3\)
(b) Using a \(1 \%\) level of significance find the critical region of this test. You should state the probability of rejection in each tail which should be as close as possible to 0.005
(c) Write down the actual significance level of the test. The value of the observation was found to be 15 .
(d) Comment on this finding in light of your critical region.