3. A single observation \(x\) is to be taken from \(X \sim \mathrm {~B} ( 12 , p )\)
This observation is used to test \(\mathrm { H } _ { 0 } : p = 0.45\) against \(\mathrm { H } _ { 1 } : p > 0.45\)
- Using a \(5 \%\) level of significance, find the critical region for this test.
- State the actual significance level of this test.
The value of the observation is found to be 9
- State the conclusion that can be made based on this observation.
- State whether or not this conclusion would change if the same test was carried out at the
- 10\% level of significance,
- \(1 \%\) level of significance.