Suppose that in Example 1 the manufacturer of the new medication feels that the odds are 4 to 1 that with this medication the recovery rate from the disease is 0.90 rather than 0.60. With these odds, what are the probabilities that he will make a wrong decision if he uses the decision Function
Example 1
Suppose that the manufacturer of a new medication wants to test the null hypothesis θ = 0.90 against the alternative hypothesis θ = 0.60. His test statistic is X, the observed number of successes (recoveries) in 20 trials, and he will accept the null hypothesis if x > 14; otherwise, he will reject it. Find α and β.