Let p represent the proportion of a population which does not get the flu during a winter. We test a vaccine's effectiveness by giving it to 100 volunteers and observing X, the number who do not get...

Let p represent the proportion of a population which does not get

the flu during a winter. We test a vaccine's effectiveness by

giving it to 100 volunteers and observing X, the number who do

not get the flu. It is known that 3/4 of the population survives

the winter without flu if no vaccine is given.

(a) State the hypotheses H0 and H1 , so that we place the statistical burden on the vaccine to demonstrate its effectiveness.

(b) Using the normal approximation to the binomial distribution,

find the critical region for this test using a = 0.05.

(c) Again using the normal approximation to the binomial distribution, find the probability of a type II error given p =0.9