1. In the subway, right next to thestairs there's an escalator, so people can choose between takingthe stairs or taking the escalators. Suppose 20 individuals areabout to pass through. Let ???? be the probability that an individualtakes the stairs. Suppose we want to test Ho: ?????0.5 versus H1:????>0.5, and we decide to use the test ???? which rejects the nullhypothesis if Y, the number of individuals who take the stairsinstead of the escalator, is greater than 12. a. Provide anappropriate distribution for Y. Justify your answer.
2. 2. Find the power function of the test ????.
   3. Find the size of the test ????.
   4. Is the test ???? ideal? Show/justify your answer.
   5. Is the test ???? unbiased? Show/justify your answer.
   6. Suppose it was observed that 16 individuals took the stairs.Solve for the p-value.
   7. Given ????=0.05 level of significance and the computed p-value in(f) for testing ????0 vs ????1, what will your decision and conclusionbe?