A company dedicated to the manufacture of batteries affirms that the new composition with the
that the plates are made will increase the battery life by more than 70%. For
verify this statement, suppose that 100 batteries are analyzed and that the critical region is
defined as x < 82, where x is the number of batteries with plates that are made with the
new composition. (use the normal approximation)
a) Evaluate the probability of making a type I error, assuming that p = 0.7.
b) Evaluate the probability of making a type II error, for alternative p = 0.9.