Historically, the probability of surviving the Ebola virus was only 30%, but new treatments are showing amazing effectiveness (New York Times, 8/12/2019). Suppose you are testing a new treatment in a...

Historically, the probability of surviving the Ebola virus was only 30%, but new treatments are showing amazing effectiveness (New York Times, 8/12/2019). Suppose you are testing a new treatment in a sample of 10 victims.

(a) If you use α = 10%, what would you use as the rejection region for the onesided hypothesis test? (Hint: you will use the binomial distribution.)

(b) If 4 of the victims in your sample survived, what would you conclude?

(c) While you are not concerned with small increases in the probability of survival, you do want a high probability of detecting an increase in the survival rate to 60%. Using the rejection region you found in part (a), what is the power of your test in this case?