9 A pharmaceutical company is developing a new drug to treat a certain disease. The company will continue to develop the drug if the proportion \(p\) of those who have the disease and show a substantial improvement after treatment is greater than 0.7 . The company carries out a test, at the \(5 \%\) significance level, on a random sample of 14 patients who suffer from the disease.
- Find the critical region for the test.
- Given that 12 of the 14 patients in the sample show a substantial improvement, carry out the test.
- Find the probability that the test results in a Type II error if in fact \(p = 0.8\).
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